Results 21 to 30 of about 213 (54)
Strong modularity of reducible Galois representations [PDF]
, 2016 In this paper, we call strongly modular those reducible semi-simple odd mod $l$ Galois representations for which the conclusion of the strongest form of Serre's original modularity conjecture holds.
Billerey, Nicolas, Menares, Ricardo
core +4 more sources
Sturm Bounds for Siegel Modular Forms [PDF]
, 2015 We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of Siegel modular forms and properties of specializations of Jacobi forms to ...
Richter, Olav K. +1 more
core +2 more sources
Variation of anticyclotomic Iwasawa invariants in Hida families [PDF]
, 2017 Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg $L$-functions, we obtain anticyclotomic analogues of the results of Emerton-Pollack-Weston on the variation of Iwasawa ...
Castella, Francesc +2 more
core +2 more sources
On the density of the odd values of the partition function, II: An infinite conjectural framework
, 2018 We continue our study of a basic but seemingly intractable problem in integer partition theory, namely the conjecture that $p(n)$ is odd exactly $50\%$ of the time.
Judge, Samuel D., Zanello, Fabrizio
core +1 more source
On the density of the odd values of the partition function
, 2017 The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2.
Judge, Samuel D. +2 more
core +1 more source
On p-adic properties of Siegel modular forms
, 2013 We show that Siegel modular forms of level \Gamma_0(p^m) are p-adic modular forms. Moreover we show that derivatives of such Siegel modular forms are p-adic. Parts of our results are also valid for vector-valued modular forms.
Boecherer, Siegfried, Nagaoka, Shoyu
core +1 more source
Ramanujan type congruences for the Klingen-Eisenstein series
, 2014 In the case of Siegel modular forms of degree $n$, we prove that, for almost all prime ideals $\frak{p}$ in any ring of algebraic integers, mod $\frak{p}^m$ cusp forms are congruent to true cusp forms of the same weight.
Kikuta, Toshiyuki, Takemori, Sho
core +1 more source
Hecke grids and congruences for weakly holomorphic modular forms
, 2013 Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue ...
Ahlgren, Scott, Andersen, Nickolas
core +1 more source
Filtrations of dc-weak eigenforms
, 2017 The notions of strong, weak and dc-weak eigenforms mod $p^n$ was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound (that is, depending only on $p$, $n$) on dc-weak eigenforms mod $p^n$ of ...
Rustom, Nadim
core +1 more source
Slopes for higher rank Artin-Schreier-Witt Towers [PDF]
, 2016 We fix a monic polynomial $\bar f(x) \in \mathbb{F}_q[x]$ over a finite field of characteristic $p$, and consider the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower defined by $\bar f(x)$; this is a tower of curves $\cdots \to C_m \to C_{m-1} \to ...
Ren, Rufei +3 more
core +1 more source