Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions: III

Masanori Katsurada, Kohji Matsumoto

研究成果: Article査読

1 被引用数 (Scopus)

抄録

The main object of this paper is the mean square Ih(s) of higher derivatives of Hurwitz zeta functions ζ(s,α). We shall prove asymptotic formulas for Ih(1/2 + it) as t → + +∞ with the coefficients in closed expressions (Theorem 1). We also prove a certain explicit formula for Ih(1/2 + it) (Theorem 2), in which the coefficients are, in a sense, not explicit. However, one merit of this formula is that it contains sufficient information for obtaining the complete asymptotic expansion for Ih(1/2 + it) when h is small. Another merit is that Theorem 1 can be strengthened with the aid of Theorem 2 (see Theorem 3). The fundamental method for the proofs is Atkinson's dissection argument applied to the product ζ(u,α)ζ(v,α) with the independent complex variables u and v.

本文言語English
ページ(範囲)239-266
ページ数28
ジャーナルCompositio Mathematica
131
3
DOI
出版ステータスPublished - 2002

ASJC Scopus subject areas

  • 代数と数論

フィンガープリント

「Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions: III」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル