2 citations · 2 across the 6 of their papers we have counts for
6 papers
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…
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…
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…
Kampé de Fériet hypergeometric functions over finite fields
Ryojun Ito, Satoshi Kumabe, Akio Nakagawa +1
Kampé de Fériet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell's functions. It is known that they satisfy many reduction a…
Appell-Lauricella hypergeometric functions over finite fields and algebraic varieties
Akio Nakagawa
We prove finite field analogues of integral representations of Appell- Lauricella hypergeometric functions in many variables. We consider certain hypersurfaces having a group actio…
Artin -functions of diagonal hypersurfaces and generalized hypergeometric functions over finite fields
Akio Nakagawa
We compute the Artin -function of a diagonal hypersurface D_λ over a finite field associated to a character of a finite group acting on D_λ , and under some condition, express i…