3 papers
math.NT2024
Maximal order for divisor functions and zeros of the Riemann zeta-function
Hirotaka Akatsuka
Ramanujan investigated maximal order for the number of divisors function by introducing some notion such as (superior) highly composite numbers. He also studied maximal order for o…
math.NT2024
An asymptotic property on a reciprocity law for the Bettin--Conrey cotangent sum
Hirotaka Akatsuka, Yuya Murakami
In 2013 Bettin and Conrey have introduced a cotangent sum , which can be regarded as a variant of the Dedekind sum. They have discovered tha…
math.NT2016
Zeros of the first derivative of Dirichlet -functions
Hirotaka Akatsuka, Ade Irma Suriajaya
Yıldırım has classified zeros of the derivatives of Dirichlet -functions into trivial zeros, nontrivial zeros and vagrant zeros. In this paper we remove the possibility of vagra…