10 citations · 16 across the 14 of their papers we have counts for
16 papers
On -congruences for meromorphic modular forms with supersingularity
Kathrin Bringmann, Pavel Guerzhoy, Ben Kane +2
In this paper, we investigate congruences for meromorphic modular forms which have a pole at a single point in the fundamental domain of . For a p…
Congruences for traces of singular moduli and Hurwitz - Kronecker class numbers
Pavel Guerzhoy
Traces of singular moduli were introduced and studied by Zagier in 1998. Being simultaneously the (traces of) values of a modular function (-invariant) and Fourier coefficients…
Non-vanishing of a certain quantity related to the p-adic coupling of mock modular forms with newforms
Pavel Guerzhoy
Several authors have recently proved results which express a cusp form as a -adic limit of weakly holomorphic modular forms under repeated application of Atkin's -operator. I…
On the -adic values of the weight two Eisenstein series for supersingular primes
Pavel Guerzhoy
The weight two Eisenstein series may be considered as the first example of a Katz -adic modular form. Classically, its values are defined for the primes of ordinary reduction. W…
Deep hole lattices and isogenies of elliptic curves
Lenny Fukshansky, Pavel Guerzhoy, Tanis Nielsen
Given a lattice in the plane, we define the affiliated deep hole lattice to be spanned by a shortest vector of and a deep hole of contained in the triangle with…
A very special case of Siegel's mass formula and Hecke operators
Pavel Guerzhoy, Ben Kane
We make use of Hecke operators and arithmetic of imaginary quadratic fields to derive an explicit version of a special case of Siegel's mass formula.
On sparse geometry of numbers
Lenny Fukshansky, Pavel Guerzhoy, Stefan Kuehnlein
Let be a lattice of full rank in -dimensional real space. A vector in is called -sparse if it has no more than nonzero coordinates. We define the -th successiv…
Periodicities for Taylor coefficients of half-integral weight modular forms
Pavel Guerzhoy, Michael H. Mertens, Larry Rolen
Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Ta…
Farkas' identities with quartic characters
Pavel Guerzhoy, Ka Lun Wong
Farkas in \cite{Farkas} introduced an arithmetic function and found an identity involving and a sum of divisor function . The first-named author and Raji in \cite{Guerz…
Central -values of elliptic curves and local polynomials
Stephan Ehlen, Pavel Guerzhoy, Ben Kane +1
Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of -functions. In particular, we find finite formulas for certai…
On arithmetic lattices in the plane
Lenny Fukshansky, Pavel Guerzhoy, Florian Luca
We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates o…
Congruences for Taylor expansions of quantum modular forms
Pavel Guerzhoy, Zachary Kent, Larry Rolen
Recently, a beautiful paper of Andrews and Sellers has established linear congruences for the Fishburn numbers modulo an infinite set of primes. Since then, a number of authors hav…
Shintani lifts and fractional derivatives for harmonic weak Maass forms
Kathrin Bringmann, Pavel Guerzhoy, Ben Kane
In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by diffe…
On cycle integrals of weakly holomorphic modular forms
Kathrin Bringmann, Pavel Guerzhoy, Ben Kane
In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms. We use th…
Mock modular forms as -adic modular forms
Kathrin Bringmann, Pavel Guerzhoy, Ben Kane
In this paper, we consider the question of correcting mock modular forms in order to obtain -adic modular forms. In certain cases we show that a mock modular form is a …
Some congruences for traces of singular moduli
Pavel Guerzhoy
We address a question posed by Ono, prove a general result for powers of an arbitrary prime, and provide an explanation for the appearance of higher congruence moduli for certain s…