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Karin Ikeda

Publications and source records attributed to Karin Ikeda.

5 recordsLinked to original sources
arXiv2025

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function

In 1997, Báez-Duarte gave a probabilistic proof of the asymptotic formula for the partition function, which had originally been proved by Hardy-Ramanujan. Based on the probabilistic approach, this paper proves an asymptotic formula for the coefficients of the elliptic modular $j$-function using various expressions in terms of modular functions having simple infinite products.

math.NT↗
arXiv2024

Hurwitz-Lerch type central binomial series

The central binomial series is a subject that has been extensively studied, for example in the context of the irrationality of Riemann zeta values. In this paper, the Hurwitz version of the central binomial series is defined by adding one real parameter, and its values at integer points are studied.

math.NT↗
arXiv2023

On real zeros of the Hurwitz zeta function

In this paper, we present results on the uniqueness of the real zeros of the Hurwitz zeta function in given intervals. The uniqueness in question, if the zeros exist, has already been proved for the intervals $(0,1)$ and $(-N, -N+1)$ for $N \geq 5$ by Endo-Suzuki and Matsusaka respectively. We prove the uniqueness of the real zeros in the remaining intervals by examining the behavior of certain associated polynomials.

math.NT↗