ON THE GENERAL TRANSFORMATION OF THE WIRTINGER INTEGRAL

Watanabe, Humihiko

doi:info:doi/10.18910/29198

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タイトル	ON THE GENERAL TRANSFORMATION OF THE WIRTINGER INTEGRAL
著者	Watanabe, Humihiko Watanabe, Humihiko
抄録	The Wirtinger integral is the uniformization to the upper half plane H of the hypergeometric function defined on the complex projective line P^1. In [5] we established the transformation formulas of the Wirtinger integral for the linear fractional transformations τ → τ + 2 and τ → -1/τ with the aide of the theory of theta functions. As a corollary we obtain the transformation formulas of the Wirtinger integral for the linear fractional transformations τ → τ + 2 and τ → τ/(-2τ + 1) which are identified with generators of the principal congruence subgroup Γ(2) modulo center. These formulas correspond to the monodromy matrices of the hypergeometric function for generators of the fundamental group of P^1 minus three points. The purpose of this paper is to generalize this result, that is, we establish the transformation formula of the Wirtinger integral for a general element (a b c d) of Γ (2), which corresponds to a general monodromy matrix of the hypergeometric function.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	51
号	2
開始ページ	425
終了ページ	438
刊行年月	2014-04
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/29198
言語	英語
DOI	info:doi/10.18910/29198
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 51, Number 2　(2014-4）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.51(2) P.425-P.438
DC.title	ON THE GENERAL TRANSFORMATION OF THE WIRTINGER INTEGRAL
DC.creator	Watanabe, Humihiko
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2014-04
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/29198
DCTERMS.abstract	The Wirtinger integral is the uniformization to the upper half plane H of the hypergeometric function defined on the complex projective line P^1. In [5] we established the transformation formulas of the Wirtinger integral for the linear fractional transformations τ → τ + 2 and τ → -1/τ with the aide of the theory of theta functions. As a corollary we obtain the transformation formulas of the Wirtinger integral for the linear fractional transformations τ → τ + 2 and τ → τ/(-2τ + 1) which are identified with generators of the principal congruence subgroup Γ(2) modulo center. These formulas correspond to the monodromy matrices of the hypergeometric function for generators of the fundamental group of P^1 minus three points. The purpose of this paper is to generalize this result, that is, we establish the transformation formula of the Wirtinger integral for a general element (a b c d) of Γ (2), which corresponds to a general monodromy matrix of the hypergeometric function.
DC.identifier	info:doi/10.18910/29198
citation_title	ON THE GENERAL TRANSFORMATION OF THE WIRTINGER INTEGRAL
citation_author	Watanabe, Humihiko
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2014-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	51
citation_issue	2
citation_firstpage	425
citation_lastpage	438
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/29198
citation_doi	info:doi/10.18910/29198

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