Results 31 to 40 of about 450 (80)

Congruences for traces of singular moduli

, 2004
We extend a result of Ahlgren and Ono on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.Comment: 8 pages, to appear in The Ramanujan ...
Osburn, Robert
core   +1 more source

"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

A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds [PDF]

, 2018
We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least conjecturally, from the ...
Zudilin, Wadim
core   +4 more sources

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

Modularity of trianguline Galois representations

Forum of Mathematics, Sigma
We use the theory of trianguline $(\varphi ,\Gamma )$ -modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients.
Rebecca Bellovin
doaj   +1 more source

Higher congruence companion forms [PDF]

, 2012
For a rational prime $p \geq 3$ we consider $p$-ordinary, Hilbert modular newforms $f$ of weight $k\geq 2$ with associated $p$-adic Galois representations $\rho_f$ and $\mod{p^n}$ reductions $\rho_{f,n}$.
Adibhatla, Rajender, Manoharmayum, Jayanta   +1 more
core   +2 more sources

Congruences Among Power Series Coefficients of Modular Forms [PDF]

, 2013
Many authors have investigated the congruence relations amongst the coefficients of power series expansions of modular forms $f$ in modular functions $t$. In a recent paper, R. Osburn and B. Sahu examine several power series expansions and prove that the
Moy, Richard
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

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

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