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.
core +1 more source
Weakly holomorphic modular forms in prime power levels of genus zero
, 2017 Let $M_k^\sharp(N)$ be the space of weight $k$, level $N$ weakly holomorphic modular forms with poles only at the cusp at $\infty$. We explicitly construct a canonical basis for $M_k^\sharp(N)$ for $N\in\{8,9,16,25\}$, and show that many of the Fourier ...
Da Silva, Caroline M. +3 more
core +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
Local-global compatibility for l=p, II
, 2011 We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an
Barnet-Lamb, Thomas +3 more
core +3 more sources
A characterization of ordinary modular eigenforms with CM [PDF]
, 2013 For a rational prime $p \geq 3$ we show that a $p$-ordinary modular eigenform $f$ of weight $k\geq 2$, with $p$-adic Galois representation $\rho_f$, mod ${p^m}$ reductions $\rho_{f,m}$, and with complex multiplication (CM), is characterized by the ...
Adibhatla, Rajender +1 more
core +1 more source
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
core +1 more source
Construction of some families of 2-dimensional crystalline representations
, 2003 We construct explicitly some analytic families of etale (phi,Gamma)-modules, which give rise to analytic families of 2-dimensional crystalline representations.
Berger, Laurent +2 more
core +3 more sources
Converse theorems and the local Langlands correspondence in families. [PDF]
Invent Math, 2018 Helm D, Moss G.
europepmc +1 more source
Congruences for the coefficients of weakly holomorphic modular forms
, 2006 Stephanie Treneer
semanticscholar +1 more source
Influenza virus surveillance in Argentina during the 2012 season: antigenic characterization, genetic analysis and antiviral susceptibility. [PDF]
Epidemiol Infect, 2016 Benedetti E +10 more
europepmc +1 more source