19 citations · 38 across the 9 of their papers we have counts for
8 papers · 1 filter
-adic properties and congruences of -regular partition functions
Ahmad El-Guindy, Mostafa M. Ghazy
We study -regular partitions by defining a sequence of modular forms of level and quadratic character which encode their -adic behavior. We show that this sequen…
Equidistribution of Gross points over rational function fields
Ahmad El-Guindy, Riad Masri, Matthew Papanikolas +1
In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field . We apply this result to study the reduction map from C…
Explicit formulas and vanishing conditions for certain coefficients of Drinfeld-Goss Hecke eigenforms
Ahmad El-Guindy
We obtain a closed form polynomial expression for certain coefficients of Drinfeld-Goss double-cuspidal modular forms which are eigenforms for the degree one Hecke operators with p…
Log-algebraic identities on Drinfeld modules and special L-values
Chieh-Yu Chang, Ahmad El-Guindy, Matthew A. Papanikolas
We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring F_q[theta]. This generalizes results of Anderson for the rank…
Legendre Drinfeld modules and universal supersingular polynomials
Ahmad El-Guindy
We introduce a certain family of Drinfeld modules that we propose as analogues of the Legendre normal form elliptic curves. We exhibit explicit formulas for a certain period of suc…
On symmetric powers of -recurrent sequences and deformations of Eisenstein series
Ahmad El-Guindy, Aleksandar Petrov
We prove the equality of several -recurrent sequences, which were first considered by Pellarin, and which have close connections to Drinfeld vectorial modular forms. Our result…
Identities for Anderson generating functions for Drinfeld modules
Ahmad El-Guindy, Matthew A. Papanikolas
Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and l…
Explicit formulas for Drinfeld modules and their periods
Ahmad El-Guindy, Matthew A. Papanikolas
We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well known formulas for the Carlitz exponenti…