Results 11 to 20 of about 278 (30)
Twist‐minimal trace formulas and the Selberg eigenvalue conjecture
Journal of the London Mathematical Society, Volume 102, Issue 3, Page 1067-1134, December 2020., 2020 Abstract We derive a fully explicit version of the Selberg trace formula for twist‐minimal Maass forms of weight 0 and arbitrary conductor and nebentypus character, and apply it to prove two theorems. First, conditional on Artin's conjecture, we classify the even 2‐dimensional Artin representations of small conductor; in particular, we show that the ...
Andrew R. Booker +2 more
wiley +1 more source
Base change for Elliptic Curves over Real Quadratic Fields [PDF]
, 2014 Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.Comment: added a short proof of Proposition 2.1 and a few more small changes to improve ...
Dieulefait, Luis, Freitas, Nuno
core +4 more sources
Elliptic Curves over Totally Real Cubic Fields are Modular [PDF]
, 2019 We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to
Derickx, Maarten +2 more
core +2 more sources
Criteria for irreducibility of mod p representations of Frey curves [PDF]
, 2014 Let K be a totally real Galois number field and let A be a set of elliptic curves over K. We give sufficient conditions for the existence of a finite computable set of rational primes P such that for p not in P and E in A, the representation on E[p] is ...
Freitas, Nuno, Siksek, Samir
core +3 more sources
On Serre's uniformity conjecture for semistable elliptic curves over totally real fields [PDF]
, 2015 Let $K$ be a totally real field, and let $S$ be a finite set of non-archimedean places of $K$. It follows from the work of Merel, Momose and David that there is a constant $B_{K,S}$ so that if $E$ is an elliptic curve defined over $K$, semistable outside
Anni, Samuele, Siksek, Samir
core +4 more sources
, 2011 The notion of adequate subgroups was introduced by Jack Thorne. It is a weakening of the notion of big subgroup used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois representations.
Guralnick, Robert
core +2 more sources
Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations [PDF]
, 2010 We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4,Z). Among these are the usual group cohomology, the Tate-Farrell cohomology, and the homology of the sharbly complex.
Ash, Avner +2 more
core +2 more sources
On a variation of the Erdős–Selfridge superelliptic curve
Bulletin of the London Mathematical Society, Volume 51, Issue 4, Page 633-638, August 2019., 2019 Abstract In a recent paper by Das, Laishram and Saradha, it was shown that if there exists a rational solution of yl=(x+1)…(x+i−1)(x+i+1)…(x+k) for i not too close to k/2 and y≠0, then logl<3k. In this paper, we extend the number of terms that can be missing in the equation and remove the condition on i.
Sam Edis
wiley +1 more source
Residual Representations of Semistable Principally Polarized Abelian Varieties [PDF]
, 2016 Let $A$ be a semistable principally polarized abelian variety of dimension $d$ defined over the rationals. Let $\ell$ be a prime and let $\bar{\rho}_{A,\ell} : G_{\mathbb{Q}} \rightarrow \mathrm{GSp}_{2d}(\mathbb{F}_\ell)$ be the representation giving ...
Anni, Samuele +2 more
core +3 more sources
Tamagawa defect of Euler systems [PDF]
, 2007 As remarked in [Kolyvagin systems, by Barry Mazur and Karl Rubin] Proposition 6.2.6 and Buyukboduk[ arXiv:0706.0377v1 ] Remark 3.25 one does not expect the Kolyvagin system obtained from an Euler system for a p-adic Galois representation T to be ...
Abbes +18 more
core +2 more sources