77 citations · 188 across the 17 of their papers we have counts for
6 papers · 1 filter
The trace of Frobenius of elliptic curves and the -adic gamma function
Dermot McCarthy
We define a function in terms of quotients of the -adic gamma function which generalizes earlier work of the author on extending hypergeometric functions over finite fields to t…
A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform
Dermot McCarthy, Matthew A. Papanikolas
Although links between values of finite field hypergeometric functions and eigenvalues of elliptic modular forms are well known, we establish in this paper that there are also conn…
On a supercongruence conjecture of Rodriguez-Villegas
Dermot McCarthy
In examining the relationship between the number of points over on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of…
Extending Gaussian hypergeometric series to the -adic setting
Dermot McCarthy
We define a function which extends Gaussian hypergeometric series to the -adic setting. This new function allows results involving Gaussian hypergeometric series to be extended…
Binomial coefficient-harmonic sum identities associated to supercongruences
Dermot McCarthy
We establish two binomial coefficient--generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of n…
Transformations of Well-Poised Hypergeometric Functions over Finite Fields
Dermot McCarthy
We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transform…