Výsledky vyhledávání - "Akatsuka, Hirotaka"

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Maximal order for divisor functions and zeros of the Riemann zeta-function

Autor: Akatsuka, Hirotaka

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 other arithmetic functions including the sum of powers of divisors func

Externí odkaz: http://arxiv.org/abs/2411.19259

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An asymptotic property on a reciprocity law for the Bettin--Conrey cotangent sum

Autor: Akatsuka, Hirotaka, Murakami, Yuya

In 2013 Bettin and Conrey have introduced a cotangent sum $c \colon \mathbb{Q}_{>0}\to \mathbb{R}$, which can be regarded as a variant of the Dedekind sum. They have discovered that the cotangent sum satisfies a kind of reciprocity laws. Roughly spea

Externí odkaz: http://arxiv.org/abs/2402.14216

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Zeros of the first derivative of Dirichlet $L$-functions

Autor: Akatsuka, Hirotaka, Suriajaya, Ade Irma

Publikováno v: J. Number Theory 184 (2018), 300-329

Y\i ld\i r\i m has classified zeros of the derivatives of Dirichlet $L$-functions into trivial zeros, nontrivial zeros and vagrant zeros. In this paper we remove the possibility of vagrant zeros for $L'(s,\chi)$ when the conductors are large to some

Externí odkaz: http://arxiv.org/abs/1604.08015

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