D. McCarthy

activity

20072024

most citedA p-adic analogue of a formula of Ramanujan

77 citations · 188 across the 17 of their papers we have counts for

collaborators

19 papers

math.NT2024

Splitting Hypergeometric Functions over Roots of Unity

Dermot McCarthy, Mohit Tripathi

We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of l…

math.NT2023

The number of $F_{q}$ -points on diagonal hypersurfaces with monomial deformation

Dermot McCarthy

We consider the family of diagonal hypersurfaces with monomial deformation $D_{d, λ, h} : x_{1}^{d} + x_{2}^{d} \dots + x_{n}^{d} - d λ x_{1}^{h_{1}} x_{2}^{h_{2}} \dots x_{n}^{h_{n}} = 0$ where $d = h_1…

math.NT2021

Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures

Madeline Locus Dawsey, Dermot McCarthy

Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their general…

math.NT2020

Generalized Paley graphs and their complete subgraphs of orders three and four

Madeline Locus Dawsey, Dermot McCarthy

Let $k \geq 2$ be an integer. Let $q$ be a prime power such that $q \equiv 1 (mod k)$ if $q$ is even, or, $q \equiv 1 (mod 2 k)$ if $q$ is odd. The generalized Paley graph of or…

math.NT2018

Apéry-like numbers and families of newforms with complex multiplication

Alexis Gomez, Dermot McCarthy, Dylan Young

Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by $Q (- 3)$ and the other by $Q (- 2)$ . The val…

math.NT2017★ 9 cited

Sequences, modular forms and cellular integrals

Dermot McCarthy, Robert Osburn, Armin Straub

It is well-known that the Apéry sequences which arise in the irrationality proofs for $ζ (2)$ and $ζ (3)$ satisfy many intriguing arithmetic properties and are related to the $p$ th F…