Asymptotic expansions for double Shintani zeta-functions of several variables

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

This is a summarized version of the forthcoming paper [19]. Let m and n be any positive integers. We write e(x)=e√-1, and use the vectorial notation x=(x1,...,xm) for any complex x and xi(i=1,...,m). The main object of this paper is the Shintani zeta-function φ̃n(s,a,λ;z) defined by (1.4) below, where sj(j=1,...,n) are complex variables, ai and λi(i=1,2) real parameters with ai>0, and z j complex parameters with |argzj|<π(j=1,...,n). We shall first present a complete asymptotic expansion of φ̃ n(s,a,λ;z) in the ascending order of zn as z n→0 (Theorem 1), and that in the descending order of z n as zn→∞ (Theorem 2), both through the sectorial region |argzn0|<π/2 for any angle θ0 with |θ0|<π/2, while other z j's move within the same sector upon satisfying the conditions z j≈zn(j=1,...,n-1). It is significant that the Lauricella hypergeometric functions (defined by (2.1) below) appear in each term of the asymptotic series on the right sides of (2.7) and (2.10). Our main formulae (2.6) (with (2.7) and (2.8)) and (2.9) (with (2.10) and (2.11)) further yield several functional properties of φ̃n(s,a,λ;z) (Corollaries 1-3).

本文言語English
ホスト出版物のタイトルDiophantine Analysis and Related Fields 2011, DARF - 2011
ページ58-72
ページ数15
DOI
出版ステータスPublished - 2011
イベントDiophantine Analysis and Related Fields 2011, DARF - 2011 - Musashino, Tokyo, Japan
継続期間: 2011 3 32011 3 5

出版物シリーズ

名前AIP Conference Proceedings
1385
ISSN(印刷版)0094-243X
ISSN(電子版)1551-7616

Other

OtherDiophantine Analysis and Related Fields 2011, DARF - 2011
国/地域Japan
CityMusashino, Tokyo
Period11/3/311/3/5

ASJC Scopus subject areas

  • 物理学および天文学(全般)

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