5 papers
An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular -function
Karin Ikeda
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 probabilisti…
Hurwitz-Lerch type central binomial series
Karin Ikeda, Yuta Kadono
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 versi…
The average number of Goldbach representations over multiples of
Karin Ikeda, Ade Irma Suriajaya
We discuss the evaluation of the average number of Goldbach representations for integers which are multiples of introduced by Granville. We improve an estimate given by Granvil…
On real zeros of the Hurwitz zeta function
Karin Ikeda
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 b…
Multiple zeta values and Euler's reflection formula for the gamma function
Karin Ikeda, Mika Sakata
In this paper, we give a purely algebraic proof of an identity coming directly from Euler's reflection formula for the gamma function. Our proof uses Hoffman's harmonic algebra and…