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 41 to 60 of 70     1 2 3 4     Modular forms and the inverse Galois problemWiese, Gabor Presentation (2013, January 17)Detailed reference viewed: 18 (1 UL) Equidistribution of signs for modular eigenforms of half integral weightInam, Ilker; Wiese, Gabor in Archiv der Mathematik [=ADM] (2013), 101(4), 331--339Let f be a cusp form of weight k+1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. We study an equidistribution conjecture of Bruinier and Kohnen for the signs of ... [more ▼]Let f be a cusp form of weight k+1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. We study an equidistribution conjecture of Bruinier and Kohnen for the signs of a(n). We prove this conjecture for certain subfamilies of coefficients that are accessible via the Shimura lift by using the Sato-Tate equidistribution theorem for integral weight modular forms. Firstly, an unconditional proof is given for the family {a(tp^2)}_p where t is a squarefree number and p runs through the primes. In this case, the result is in terms of natural density. To prove it for the family {a(tn^2)}_n where t is a squarefree number and n runs through all natural numbers, we assume the existence of a suitable error term for the convergence of the Sato-Tate distribution, which is weaker than one conjectured by Akiyama and Tanigawa. In this case, the results are in terms of Dedekind-Dirichlet density. [less ▲]Detailed reference viewed: 43 (4 UL) Algèbre 1 (BASI filière mathématiques, 2013)Wiese, Gabor ; David, Agnès Learning material (2013)Lecture notes written in French from the Algebra 1 lecture in the 1st term of the Bachelor programme BASI branch Mathematics at the University of Luxembourg. The lecture starts with preliminaries on logic ... [more ▼]Lecture notes written in French from the Algebra 1 lecture in the 1st term of the Bachelor programme BASI branch Mathematics at the University of Luxembourg. The lecture starts with preliminaries on logic, sets and functions, it builds the natural numbers (almost) from the Peano axioms, then constructs the integers and the rationals. Groups and rings are introduced in that context. The most basic definitions and results from abstract linear algebra are also given. The course finishes with some basic group theory. [less ▲]Detailed reference viewed: 49 (1 UL) Commutative Algebra (Master in Mathematics, 2013)Wiese, Gabor Learning material (2013)Lecture notes from the 1st year of Master in Mathematics at the University of Luxembourg. Rings of integers of number fields and coordinate rings of plane curves are the central examples around which the ... [more ▼]Lecture notes from the 1st year of Master in Mathematics at the University of Luxembourg. Rings of integers of number fields and coordinate rings of plane curves are the central examples around which the theory is developed: integrality, noetherian rings, localisation, Noether normalisation, Hilbert's Nullstellensatz, etc. [less ▲]Detailed reference viewed: 52 (2 UL) On modular Galois representations modulo prime powersChen, Imin; Kiming, Ian; Wiese, Gabor in International Journal of Number Theory (2013), 9(1), 91--113We study modular Galois representations mod p^m. We show that there are three progressively weaker notions of modularity for a Galois representation mod p^m: we have named these strongly', weakly', and ... [more ▼]We study modular Galois representations mod p^m. We show that there are three progressively weaker notions of modularity for a Galois representation mod p^m: we have named these strongly', weakly', and dc-weakly' modular. Here, dc' stands for divided congruence' in the sense of Katz and Hida. These notions of modularity are relative to a fixed level M. Using results of Hida we display a stripping-of-powers of p away from the level' type of result: A mod p^m strongly modular representation of some level Np^r is always dc-weakly modular of level N (here, N is a natural number not divisible by p). We also study eigenforms mod p^m corresponding to the above three notions. Assuming residual irreducibility, we utilize a theorem of Carayol to show that one can attach a Galois representation mod p^m to any dc-weak' eigenform, and hence to any eigenform mod p^m in any of the three senses. We show that the three notions of modularity coincide when m=1 (as well as in other, particular cases), but not in general. [less ▲]Detailed reference viewed: 44 (3 UL) Winter School on Galois Theory, Volume 2Wiese, Gabor ; Arias De Reyna Dominguez, Sara ; Bary-Soroker, LiorBook published by University of Luxembourg / Campus Kirchberg (2013)Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal ... [more ▼]Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal "Travaux mathématiques" unites four instructional texts that have grown out of lectures delivered at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. It also includes one research article. Gebhard Böckle's contribution is a quite comprehensive survey on Galois representations. It focusses on the key ideas, and the long list of recommended references enables the reader to pursue himself/herself any of the mentioned topics in greater depth. Michael Schein's notes sketch the proof due to Khare and Wintenberger of one of the major theorems in arithmetic algebraic geometry in recent years, namely Serre's Modularity Conjecture. Moshe Jarden's contribution is based on his book on algebraic patching. It develops the method of algebraic patching from scratch and gives applications in contemporary Galois theory. David Harbater's text is complementary to Jarden's notes, and describes recent applications of patching in other aspects of algebra, for example: differential algebra, local-global principles, quadratic forms, and more. The focus is on the big picture and on providing the reader with intuition. The research article by Wulf-Dieter Geyer and Moshe Jarden concerns model completeness of valued PAC fields. [less ▲]Detailed reference viewed: 127 (9 UL) Winter School on Galois Theory, Volume 1Wiese, Gabor ; Arias De Reyna Dominguez, Sara ; Bary-Soroker, LiorBook published by University of Luxembourg / Campus Kirchberg (2013)Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal ... [more ▼]Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal "Travaux mathématiques" unites two instructional texts that have grown out of lectures delivered at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. The contribution by Wulf-Dieter Geyer is about "Field Theory". It can be considered as a textbook in its own right. It manages to start at the level that any student possesses after any introductory algebra course and nevertheless to lead the reader to very advanced field theory at the frontier of current research, and to cover a wealth of material. Many examples are contained, which nicely enlighten the presented concepts, very often providing counterexamples that show why certain hypotheses are necessary. One also finds a chapter on the history of field theory as well as other historical remarks throughout the text. The second contribution addresses "Profinite Groups". It is written by Luis Ribes, who is the author of two standard books on this subject. Being necessarily much shorter than the two books, it has the feature of presenting an overview stressing the main concepts and the links with Galois Theory. Since for those proofs which are not included precise references are given, the notes, due to their conciseness and nevertheless great amount of material, constitute an excellent starting point for any Master or PhD student willing to learn this subject. [less ▲]Detailed reference viewed: 155 (18 UL) An Application of Maeda's Conjecture to the Inverse Galois ProblemWiese, Gabor in Mathematical Research Letters (2013), 20(5), 985-993It is shown that Maeda's conjecture on eigenforms of level 1 implies that for every positive even d and every p in a density-one set of primes, the simple group PSL_2(F_{p^d}) occurs as the Galois group ... [more ▼]It is shown that Maeda's conjecture on eigenforms of level 1 implies that for every positive even d and every p in a density-one set of primes, the simple group PSL_2(F_{p^d}) occurs as the Galois group of a number field ramifying only at p. [less ▲]Detailed reference viewed: 48 (4 UL) Modulformen und das inverse Galois-ProblemWiese, Gabor Scientific Conference (2012, September 19)Detailed reference viewed: 16 (0 UL) On modular Galois representations modulo prime powersWiese, Gabor Presentation (2012, May 30)Detailed reference viewed: 12 (1 UL) Symplectic Galois representations and applications to the inverse Galois problemWiese, Gabor Presentation (2012, May 30)Detailed reference viewed: 10 (0 UL) Modulare Galois-Darstellungen und ComputeralgebraWiese, Gabor Scientific Conference (2012, May 12)Detailed reference viewed: 18 (0 UL) Four lectures on modular forms and Galois representationsWiese, Gabor Presentation (2012, February)Detailed reference viewed: 20 (0 UL) Symplectic Galois representations and applications to the inverse Galois problemWiese, Gabor Presentation (2012, January 19)Detailed reference viewed: 13 (0 UL) Algèbre 3 (théorie des corps et théorie de Galois)Wiese, Gabor Learning material (2012)Lecture notes written in French from the Algebra 3 lecture in the 3rd term of the Bachelor programme BASI branch Mathematics (old version) at the University of Luxembourg. The lecture covers field theory ... [more ▼]Lecture notes written in French from the Algebra 3 lecture in the 3rd term of the Bachelor programme BASI branch Mathematics (old version) at the University of Luxembourg. The lecture covers field theory and Galois theory and includes a treatment of the solvability of equations by radicals and a treatment of classical construction problems with ruler and compass. [less ▲]Detailed reference viewed: 80 (3 UL) Lectures on Modular Galois Representations Modulo Prime PowersWiese, Gabor Presentation (2011, December)Detailed reference viewed: 29 (3 UL) On modular forms and the inverse Galois problemDieulefait, Luis; Wiese, Gabor in Transactions of the American Mathematical Society (2011), 363(9), 4569--4584In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the ... [more ▼]In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists. [less ▲]Detailed reference viewed: 41 (2 UL) A computational study of the asymptotic behaviour of coefficient fields of modular formsMohyla, Marcel; Wiese, Gabor in Actes de la Conférence `Théorie des Nombres et Applications'' (2011)The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest ... [more ▼]The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest certain patterns, which deserve further study. [less ▲]Detailed reference viewed: 29 (0 UL) Die Serresche Modularitätsvermutung und Computer-AlgebraWiese, Gabor in Computeralgebra-Rundbrief (2010), 47In diesem Artikel für Nichtspezialisten wird die kürzlich von Khare, Wintenberger und Kisin bewiesene Serresche Modularitätsvermutung vorgestellt und ihre Bedeutung in der Computer-Algebra erläutert.Detailed reference viewed: 18 (0 UL) On mod $p$ representations which are defined over $\Bbb F_p$: IIKilford, L. J. P.; Wiese, Gabor in Glasgow Mathematical Journal (2010), 52(2), 391--400The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\chi}_{l,k} for all ... [more ▼]The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\chi}_{l,k} for all primes l, all weights k>1 and all characters \chi taking values in {+1,-1} splits completely modulo p has density 0, unconditionally for p=2 and under the Cohen-Lenstra heuristics for odd p. The method of proof is based on the construction of suitable dihedral modular forms. [less ▲]Detailed reference viewed: 25 (0 UL)     1 2 3 4