3 papers
math.NT2026
Symmetry of hypergeometric functions over finite fields and geometric interpretation
Akio Nakagawa
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geom…
math.NT2026
Special -values of certain CM weight three Hecke eigenforms
Paresh Arora, Koustav Mondal, Akio Nakagawa +1
Ramanujan's theory of elliptic functions to alternative bases connects modular forms with hypergeometric series and has led to applications such as the modularity of certain hyperg…
math.NT2024
Sum representations of Appell-Lauricella functions over finite fields using confluent hypergeometric functions and their applications
Akio Nakagawa
We prove sum representations of Appell-Lauricella functions over a finite field using confluent hypergeometric functions over the finite field. As an application, we also prove tra…