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Reductions of one-dimensional tori Perucca, Antonella in International Journal of Number Theory (2017) Detailed reference viewed: 75 (5 UL)A Short Note on the Bruinier-Kohnen Sign Equidistribution Conjecture and Halasz' Theorem ; Wiese, Gabor in International Journal of Number Theory (2016), 12(2), 357-360 In this note, we improve earlier results towards the Bruinier-Kohnen sign equidistribution conjecture for half-integral weight modular eigenforms in terms of natural density by using a consequence of ... [more ▼] In this note, we improve earlier results towards the Bruinier-Kohnen sign equidistribution conjecture for half-integral weight modular eigenforms in terms of natural density by using a consequence of Halász' Theorem. Moreover, applying a result of Serre we remove all unproved assumptions. [less ▲] Detailed reference viewed: 71 (10 UL)Criteria for p-ordinarity of Families of Elliptic curves over infinitely many number fields ; Tsaknias, Panagiotis in International Journal of Number Theory (2015), 11(1), 81-87 Detailed reference viewed: 79 (4 UL)On modular Galois representations modulo prime powers ; ; Wiese, Gabor in International Journal of Number Theory (2013), 9(1), 91--113 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 ... [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: 133 (4 UL)On modular symbols and the cohomology of Hecke triangle surfaces Wiese, Gabor in International Journal of Number Theory (2009), 5(1), 89--108 The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular ... [more ▼] The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the standard algorithms for the computation of holomorphic modular forms. Precise and explicit connections are established to the cohomology of Hecke triangle surfaces and group cohomology. In all the note a general commutative ring is used as coefficient ring in view of applications to the computation of modular forms over rings different from the complex numbers. [less ▲] Detailed reference viewed: 117 (0 UL) |
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