arXiv subjects
Publications and source records attributed to Ryojun Ito.
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 and summation formulas. In this paper, we define Kampé de Fériet hypergeometric functions over finite fields and show analogous formulas.
In this paper, we consider a modular form of weight 3, which is a product of the Borweins theta series, and express its $L$-values at $s=1$, $2$ and $3$ in terms of special values of Kampé de Fériet hypergeometric functions, which are two-variable generalization of generalized hypergeometric functions.
In this paper, we consider $L$-functions of modular forms of weight 3, which are products of the Jacobi theta series, and express their special values at $s=3$, $4$ in terms of special values of Kampé de Fériet hypergeometric functions. Moreover, via $L$-values, we give some relations between special values of Kampé de Fériet hypergeometric functions and generalized hypergeometric functions.
In this paper, we compute the special values of $L$-functions at $s=1$ of some theta products of weight $3$, and express them in terms of special values of generalized hypergeometric functions.
We consider certain CM elliptic curves which are related to Fermat curves, and express the values of $L$-functions at $s=2$ in terms of special values of generalized hypergeometric functions. We compare them and a similar result of Rogers-Zudilin with Otsubo's regulator formulas, and give a new proof of the Beilinson conjectures originally due to Bloch.