An interpolation of Bradley's sum formula
The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.
math.NT↗
arXiv subjects
Anju Yokoi
Publications and source records attributed to Anju Yokoi.
Apéry-type approximations and irrationality measures for certain $q$-series
We construct a three-parameter family of rational approximations to values of $q$-hypergeometric series. Using these approximations, we prove that, for every integer $x$ with $|x|\geq2$, the values at $r=x^{-1}$ of Ramanujan's theta function $ψ(r)=\sum_{n\geq0}r^{n(n+1)/2}$, the generating function $Δ(r)=\sum_{m\geq0}d(2m+1)r^m$ of the divisor function restricted to odd integers, and the generating function $B_4(r)=\sum_{n\geq0}b_4(n)r^n$ for $4$-regular partitions are irrational. We further obtain the upper bounds $18/7$, $18π^2/(7π^2-24)$, and $3$, respectively, for their irrationality measures. We also show that one of the constructed approximations coincides with the Padé approximation to a Lambert series due to Coussement--Smet.
math.NT↗
A functional equation for multiple zeta functions and generalized confluent hypergeometric functions
In this paper, we introduce a new function, the multiple confluent hypergeometric functions, and establish a functional equation for the $r$-variable Euler--Zagier multiple zeta functions using it. In the case when $r=2$, this functional equation includes the well-known functional equation for the Euler--Zagier double zeta functions obtained by Matsumoto.
math.NT↗
Cyclic sum formula for certain parametrized multiple zeta values
Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his problems about a generalization with three parameters.
math.NT↗