P. Guerzhoy

collaborators

4 papers

math.NT2026

On $U_{p}$ -congruences for meromorphic modular forms with supersingularity

Kathrin Bringmann, Pavel Guerzhoy, Ben Kane +2

In this paper, we investigate congruences for meromorphic modular forms $F$ which have a pole at a single point $z$ in the fundamental domain of $SL_{2} (Z)$ . For a p…

math.NT2026

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 ( $j$ -invariant) and Fourier coefficients…

math.NT2025

Cusp forms as $p$ -adic limits circumventing $p$ -adic version of the Legendre period relation

Pavel Guerzhoy

Several authors have recently proved results which express a cusp form as a $p$ -adic limit of weakly holomorphic modular forms under repeated application of Atkin's $U$ -operator. I…

math.NT2025

On the $p$ -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 $p$ -adic modular form. Classically, its values are defined for the primes of ordinary reduction. W…

On Up​-congruences for meromorphic modular forms with supersingularity

Congruences for traces of singular moduli and Hurwitz - Kronecker class numbers

Cusp forms as p-adic limits circumventing p-adic version of the Legendre period relation

On the p-adic values of the weight two Eisenstein series for supersingular primes

On $U_{p}$ -congruences for meromorphic modular forms with supersingularity

Cusp forms as $p$ -adic limits circumventing $p$ -adic version of the Legendre period relation

On the $p$ -adic values of the weight two Eisenstein series for supersingular primes