Asymptotic expansions for double Shintani zeta-functions of several variables

研究成果: Conference contribution

1 引用 (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).

元の言語English
ホスト出版物のタイトルAIP Conference Proceedings
ページ58-72
ページ数15
1385
DOI
出版物ステータス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

Other

OtherDiophantine Analysis and Related Fields 2011, DARF - 2011
Japan
Musashino, Tokyo
期間11/3/311/3/5

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expansion
theorems
asymptotic series
complex variables
hypergeometric functions
integers
coding
sectors

ASJC Scopus subject areas

  • Physics and Astronomy(all)

これを引用

Asymptotic expansions for double Shintani zeta-functions of several variables. / Katsurada, Masanori.

AIP Conference Proceedings. 巻 1385 2011. p. 58-72.

研究成果: Conference contribution

Katsurada, M 2011, Asymptotic expansions for double Shintani zeta-functions of several variables. : AIP Conference Proceedings. 巻. 1385, pp. 58-72, Diophantine Analysis and Related Fields 2011, DARF - 2011, Musashino, Tokyo, Japan, 11/3/3. https://doi.org/10.1063/1.3630041
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