Results 21 to 30 of about 396 (44)

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

Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4 [PDF]

, 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   +3 more sources

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

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

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., Westerholt-Raum, Martin   +1 more
core   +2 more sources

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

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  

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

Higher congruence companion forms [PDF]

, 2011
For a rational prime p 3 we consider p-ordinary, Hilbert modular newforms f of weight k 2 with associated p-adic Galois representations f and mod pn reductions f;n.
Adibhatla, Rajender, Manoharmayum, Jayanta   +1 more
core   +1 more source