For the purposes of this paper supercongruences are congruences between terminating
hypergeometric series and quotients of p-adic Gamma functions that are stronger than those …

Building on the developments of many people including Evans, Greene, Katz, McCarthy,
Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type …

In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp
forms in certain instances related to arithmetic triangle groups. These expressions are in …

In this paper, we investigate the relationships among hypergeometric series, truncated
hypergeometric series, and Gaussian hypergeometric functions through some families of …

POINTS ON CURVES Page 1 POINTS ON CURVES LEVENT HASAN ALi ALPÖGE
ADissertation PRESENTED TO THE FACULTY OF PRINCETON UNIVERSITY IN …

A well-known formula of Whipple relates certain hypergeometric values 7 F 6 (1) and 4 F 3
(1). In this paper, we revisit this relation from the viewpoint of the underlying hypergeometric …

We define a finite field version of Appell–Lauricella hypergeometric functions built from
period functions in several variables, paralleling recent development by Fuselier, Long …

This is a report on recent work, with Wen-Ching Winnie Li and Ling Long. In that work
explicit formulas are given, involving hypergeometric character sums, for the traces of Hecke …

We examine the families of hypergeometric series associated to a special class of modular
hypergeometric Galois representations recently studied by Allen, Grove, Long, and Tu. The …

We give an effective proof of Faltings' theorem for curves mapping to Hilbert modular stacks
over odd-degree totally real fields. We do this by giving an effective proof of the Shafarevich …