Results 21 to 30 of about 193 (35)
"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
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
On the gaps between non-zero Fourier coefficients of cusp forms of higher weight [PDF]
, 2016 We show that if a modular cuspidal eigenform $f$ of weight $2k$ is $2$-adically close to an elliptic curve $E/\mathbb{Q}$, which has a cyclic rational $4$-isogeny, then $n$-th Fourier coefficient of $f$ is non-zero in the short interval $(X, X + cX ...
Kumar, Narasimha
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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
Height one specializations of Selmer groups [PDF]
, 2018 We provide applications to studying the behavior of Selmer groups under specialization. We consider Selmer groups associated to four dimensional Galois representations coming from (i) the tensor product of two cuspidal Hida families $F$ and $G$, (ii) its
Palvannan, Bharathwaj
core +3 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
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Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4
, 2018 We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve ...
Kiming, Ian, Rustom, Nadim
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Some new $q$-congruences for truncated basic hypergeometric series
, 2019 We provide several new $q$-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric generalizations ...
Guo, Victor J. W., Schlosser, Michael J.
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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
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