Results 31 to 40 of about 432 (61)

"Divergent" Ramanujan-type supercongruences

, 2010
"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases.
Guillera, Jesús, Zudilin, Wadim
core   +2 more sources

Companion Forms in Parallel Weight One [PDF]

, 2012
Let $p>2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a mod $p$ Galois representation to arise from a mod $p$ Hilbert modular form of parallel weight one, by proving a "companion forms ...
Andreatta, Deligne, Payman Kassaei, Toby Gee   +3 more
core   +1 more source

Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]

, 2013
We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications.
Ahlgren, Scott, Kim, Byungchan
core   +1 more source

On icosahedral Artin representations

, 2001
If ρ : Gal(Qac/Q) → GL2(C) is a continuous odd irreducible representation with nonsolvable image, then under certain local hypotheses we prove that ρ is the representation associated to a weight 1 modular form and hence that the L-function of ρ has an ...
Kevin Buzzard, M. Dickinson, N. Shepherd-barron, Richard Taylor   +3 more
semanticscholar   +1 more source

Gauss-Manin connections for p-adic families of nearly overconvergent modular forms [PDF]

, 2014
We interpolate the Gauss-Manin connection in p-adic families of nearly overconvergent modular forms. This gives a family of Maass-Shimura type differential operators from the space of nearly overconvergent modular forms of type r to the space of nearly ...
Harron, Robert, Xiao, Liang
core   +2 more sources

A remark on non-integral -adic slopes for modular forms [PDF]

, 2017
We give a sufficient condition, namely “Buzzard irregularity”, for there to exist a cuspidal eigenform which does not have integral -adic slope.Accepted ...
Bergdall, John, Pollack, R.
core  

Explicit reduction modulo p of certain 2-dimensional crystalline representations, II

, 2013
We complete the calculations begun in [BG09], using the p-adic local Langlands correspondence for GL2(Q_p) to give a complete description of the reduction modulo p of the 2-dimensional crystalline representations of G_{Q_p} of slope less than 1, when p >
Buzzard, Kevin, Gee, Toby
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

L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Forum of Mathematics, Sigma
Let $\pi $ be a cuspidal, cohomological automorphic representation of an inner form G of $\operatorname {{PGL}}_2$ over a number field F of arbitrary signature. Further, let $\mathfrak {p}$ be a prime of F such that G is split at
Lennart Gehrmann, Maria Rosaria Pati
doaj   +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