References of "Wiese, Gabor 50003330"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 84 1 2 3 4 5     Galois families of modular forms and application to weight oneArias-de-Reyna, Sara; Legrand, François; Wiese, Gabor in Israel Journal of Mathematics (2021), 244We introduce Galois families of modular forms. They are a new kind of family coming from Galois representations of the absolute Galois groups of rational function fields over the rational field. We ... [more ▼]We introduce Galois families of modular forms. They are a new kind of family coming from Galois representations of the absolute Galois groups of rational function fields over the rational field. We exhibit some examples and provide an infinite Galois family of non-liftable weight one Katz modular eigenforms over an algebraic closure of F_p for p in {3,5,7,11}. [less ▲]Detailed reference viewed: 157 (4 UL) The Hidden Lattice ProblemNotarnicola, Luca ; Wiese, Gabor E-print/Working paper (2021)We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation ... [more ▼]We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the Hidden Subset Sum Problem, whose hardness is essentially determined by that of the hidden lattice problem. We describe and compare two algorithms for the hidden lattice problem: we first adapt the algorithm by Nguyen and Stern for the hidden subset sum problem, based on orthogonal lattices, and propose a new variant, which we explain to be related by duality in lattice theory. Following heuristic, rigorous and practical analyses, we find that our new algorithm brings some advantages as well as a competitive alternative for algorithms for problems with cryptographic interest, such as Approximate Common Divisor Problems, and the Hidden Subset Sum Problem. Finally, we study variations of the problem and highlight its relevance to cryptanalysis. [less ▲]Detailed reference viewed: 43 (0 UL) On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen ConjectureInam, Ilker; Demirkol Özkaya, Zeynep; Tercan, Elif et alin Turkish Journal of Mathematics (2021), 45(6), 2427-2440This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level Gamma_0(4) and half-integral weights. Based on substantial ... [more ▼]This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level Gamma_0(4) and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently. [less ▲]Detailed reference viewed: 44 (0 UL) Algèbre linéaire 2 (BMATH 2021)Wiese, Gabor Learning material (2021)Detailed reference viewed: 163 (15 UL) Simultaneous Diagonalization of Incomplete Matrices and ApplicationsCoron, Jean-Sébastien ; Notarnicola, Luca ; Wiese, Gabor in Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), edited by Steven Galbraith, Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020 (2020, December)We consider the problem of recovering the entries of diagonal matrices {U_a}_a for a = 1, . . . , t from multiple “incomplete” samples {W_a}_a of the form W_a = P U_a Q, where P and Q are unknown matrices ... [more ▼]We consider the problem of recovering the entries of diagonal matrices {U_a}_a for a = 1, . . . , t from multiple “incomplete” samples {W_a}_a of the form W_a = P U_a Q, where P and Q are unknown matrices of low rank. We devise practical algorithms for this problem depending on the ranks of P and Q. This problem finds its motivation in cryptanalysis: we show how to significantly improve previous algorithms for solving the approximate common divisor problem and breaking CLT13 cryptographic multilinear maps. [less ▲]Detailed reference viewed: 159 (24 UL) Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod pDimitrov, Mladen; Wiese, Gabor in Journal of the Institute of Mathematics of Jussieu (2020), 19(2), 281-306The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This ... [more ▼]The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel weight 1 forms in characteristic p embed into the ordinary part of parallel weight p forms in two different ways per prime dividing p, namely via partial' Frobenius operators. MSC: 11F80 (primary); 11F41, 11F33 Keywords: Hilbert modular forms modulo p, weight one, Galois representations [less ▲]Detailed reference viewed: 105 (5 UL) Commutative Algebra (lecture notes, Master in Mathematics, Master in Secondary Education)Wiese, Gabor Learning material (2020)These are the lecture notes for the course Commutative Algebra in the Master in Mathematics and the Master in Secondary Education at the University of Luxembourg. Last update: winter term 2020.Detailed reference viewed: 211 (15 UL) Number Theory for Cryptography (Lecture Notes)Wiese, Gabor Learning material (2020)In these lectures (8 hours taught in November 2020), we mention some topics from (algebraic) number theory as well as some related concepts from (algebraic) geometry that can be useful in cryptography. We ... [more ▼]In these lectures (8 hours taught in November 2020), we mention some topics from (algebraic) number theory as well as some related concepts from (algebraic) geometry that can be useful in cryptography. We cannot go deeply into any of the topics and most results will be presented without any proofs. One of the things that one encounters are ideal lattices'. In the examples I saw, this was nothing but (an ideal in) an order in a number field, which is one of the concepts that we present here in its mathematical context (i.e. embedded in a conceptual setting). It has been noted long ago (already in the 19th century) that number fields and function fields of curves have many properties in common. Accordingly, we shall also present some basic topics on affine plane curves and their function fields. This leads us to mention elliptic curves, however, only in an affine version (instead of the better projective one); we cannot go deeply into that topic at all. The material presented here is classical and very well known. [less ▲]Detailed reference viewed: 64 (9 UL) Algèbre (notes du cours, 3ème semestre BMATH)Wiese, Gabor Learning material (2020)These are the lecture notes for the lecture Algèbre' in the 3rd semester of the Bachelor in Mathematics at the University of Luxembourg. Last update: winter term 2020.Detailed reference viewed: 137 (9 UL) Dihedral Universal DeformationsDeo, Shaunak ; Wiese, Gabor in Research in Number Theory (2020), 6This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1 ... [more ▼]This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic number theory, (3) modularity. As to (1), we prove that the universal deformation is dihedral if all infinitesimal deformations are dihedral. Concerning (2) in the setting of Galois representations of number fields, we give sufficient conditions to ensure that the universal deformation relatively unramified outside a finite set of primes is dihedral, and discuss in how far these conditions are necessary. As a side-result, we obtain cases of the unramified Fontaine-Mazur conjecture. As to (3), we prove a modularity theorem of the form R=T' for parallel weight one Hilbert modular forms for cases when the minimal universal deformation is dihedral. [less ▲]Detailed reference viewed: 157 (2 UL) Fast computation of half-integral weight modular formsInam, Ilker; Wiese, Gabor E-print/Working paper (2020)To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to have a large number of Fourier coefficients. In this article, we exhibit three bases ... [more ▼]To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to have a large number of Fourier coefficients. In this article, we exhibit three bases for the space of modular forms of any half-integral weight and level 4, which have the property that many coefficients can be computed (relatively) quickly on a computer. [less ▲]Detailed reference viewed: 38 (0 UL) Non-ramification de l'algèbre de Hecke en poids unWiese, Gabor Presentation (2019, May 09)Soit S l'espace des formes modulaires de Hilbert paraboliques en poids parallèle un géométriquement défini sur un corps fini et soit T l'algèbre de Hecke qui agit fidèlement sur S. Nous esquissons une ... [more ▼]Soit S l'espace des formes modulaires de Hilbert paraboliques en poids parallèle un géométriquement défini sur un corps fini et soit T l'algèbre de Hecke qui agit fidèlement sur S. Nous esquissons une démonstration que la représentation galoisienne à valeurs dans T est non-ramifiée au dessus de p. Ceci peut être considéré comme un premier pas vers un théorème de type R=T liant les formes modulaires de poids un et les représentations non-ramifiées au-dessus de p. Travail commun avec Shaunak Deo et Mladen Dimitrov. [less ▲]Detailed reference viewed: 47 (3 UL) Dihedral Universal DeformationsWiese, Gabor Presentation (2019, February 19)Detailed reference viewed: 69 (1 UL) Finiteness questions for Galois representationsWiese, Gabor Presentation (2019, January 29)Let p be a prime number. Due to classical work of Shimura and Deligne, to any "newform" (a modular form that is an eigenfunction for the Hecke operators and assumed of level one in the talk) one attaches ... [more ▼]Let p be a prime number. Due to classical work of Shimura and Deligne, to any "newform" (a modular form that is an eigenfunction for the Hecke operators and assumed of level one in the talk) one attaches a p-adic Galois representation. Since there are infinitely many newforms, there are infinitely many attached p-adic Galois representations. However, if one reduces them modulo p, there are only finitely many (up to isomorphism). It is tempting to ask what happens "in between", i.e. whether there is still finiteness modulo fixed prime powers. In the talk, I will motivate and explain a conjecture made with Ian Kiming and Nadim Rustom and explain partial results, including a relation to a strong question by Kevin Buzzard. The talk is based on joint work with Ian Kiming and Nadim Rustom. [less ▲]Detailed reference viewed: 63 (0 UL) MATHEMATICAL CAREERS In Luxembourg and beyondPalmirotta, Guendalina ; Notarnicola, Luca ; Wiese, Gabor Diverse speeches and writings (2019)Detailed reference viewed: 52 (1 UL) Computational Arithmetic of Modular FormsWiese, Gabor in Buyukasik, Engin; Inam, Ilker (Eds.) Notes from the International Autumn School on Computational Number Theory: Izmir Institute of Technology 2017 (2019)These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as ... [more ▼]These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted student to implement it over any ring (such that a sufficient linear algebra theory is available in the chosen computer algebra system). The chosen approach is based on group cohomology and along the way the needed tools from homological algebra are provided. [less ▲]Detailed reference viewed: 169 (3 UL) Unramifiedness of weight one Hilbert Hecke algebrasDeo, Shaunak; Dimitrov, Mladen; Wiese, Gabor E-print/Working paper (2019)We prove that the Galois pseudo-representation valued in the mod p^n parallel weight 1 Hecke algebra for GL(2) over a totally real number field F is unramified at a place above p if p-1 does not divide ... [more ▼]We prove that the Galois pseudo-representation valued in the mod p^n parallel weight 1 Hecke algebra for GL(2) over a totally real number field F is unramified at a place above p if p-1 does not divide the ramification index at that place. A novel geometric ingredient is the construction and study, in the case when p ramifies in F, of generalised Theta-operators using Reduzzi-Xiao's generalised Hasse invariants, including especially an injectivity criterion in terms of minimal weights. [less ▲]Detailed reference viewed: 69 (5 UL) Topics on modular Galois representations modulo prime powersTsaknias, Panagiotis; Wiese, Gabor in Böckle, Gebhard; Decker, Wolfram; Malle, Gunter (Eds.) Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (2018)This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes ... [more ▼]This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes algorithms and a database of modular forms orbits and higher congruences. [less ▲]Detailed reference viewed: 204 (9 UL) On the arithmetic of modular formsWiese, Gabor Presentation (2017, June 28)In this overview talk, we will illustrate the arithmetic significance of the coefficients of modular forms, from classical examples to the modern point of view of Galois representations. From that on, one ... [more ▼]In this overview talk, we will illustrate the arithmetic significance of the coefficients of modular forms, from classical examples to the modern point of view of Galois representations. From that on, one is naturally lead to questions on the distribution of the coefficients in various senses. We will briefly touch on some of them, report on recent theorems and state some open questions. When investigating arithmetical properties of coefficients through Galois representations, their ramification properties are an important object to study. One notices that forms of -so called- weight one play a special role that will be explained. The importance of Galois representations coming from modular forms is that one expects all Galois representations satisfying reasonable "geometric" assumption to arise in such a way. As a special case, we will explain the theorem of Khare and Wintenberger, formerly called Serre's modularity conjecture, and conjectural generalisations. Whereas Galois representations are usually very hard to calculate directly on a computer, modular forms are pretty simple to compute. We will briefly touch on this and what kind of information one can get. If time allows, we will also touch on an application to the so-called inverse Galois problem. [less ▲]Detailed reference viewed: 196 (1 UL) On the arithmetic of modular formsWiese, Gabor Scientific Conference (2017, June 15)In this short overview talk, we will stress the arithmetic significance of the coefficients of modular forms. This naturally leads to questions on the distribution of the coefficients in various senses ... [more ▼]In this short overview talk, we will stress the arithmetic significance of the coefficients of modular forms. This naturally leads to questions on the distribution of the coefficients in various senses. We will briefly touch on some of them and state some open questions. The arithmetic information in the coefficients of a Hecke eigenform is summarised in the attached Galois representation. When studying its ramification properties, one notices that forms of weight one play a special role that we will explain. [less ▲]Detailed reference viewed: 128 (2 UL) 1 2 3 4 5