UNIVERSALITY OF SOME FUNCTIONS RELATED TO ZETA-FUNCTIONS OF CERTAIN CUSP FORMS

Laurinčikas, Antanas; Matsumoto, Kohji; Steuding, Jörn

doi:info:doi/10.18910/26828

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タイトル	UNIVERSALITY OF SOME FUNCTIONS RELATED TO ZETA-FUNCTIONS OF CERTAIN CUSP FORMS
著者	Laurinčikas, Antanas Laurinčikas, Antanas
	Matsumoto, Kohji Matsumoto, Kohji
	Steuding, Jörn Steuding, Jörn
抄録	It is well-known that the zeta-function ζ(s,F) attached to a normalized Hecke-eigen cusp form F of weight κ is universal in the sense that their shifts ζ(s+iτ,F) with appropriate τ∈R approximate any analytic function uniformly on compact subsets of the strip {s=σ+it∈C:κ/2<σ<(κ+1)/2} with any prescribed accuracy. In this paper we consider some classes of operators Φ such that the function Φ(ζ(s,F)) is universal in the above sense. In particular, this implies the universality of the functions, for example, ζ(s,F)＾N (N-th power) and ζ^<(N)>(s,F) (N-th derivative) with N∈N, e^<ζ(s,F)>, sinζ(s,F), and cosζ(s,F).
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	4
開始ページ	1021
終了ページ	1037
刊行年月	2013-12
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/26828
言語	英語
DOI	info:doi/10.18910/26828
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 4　(2013-12）

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.50(4) P.1021-P.1037
DC.title	UNIVERSALITY OF SOME FUNCTIONS RELATED TO ZETA-FUNCTIONS OF CERTAIN CUSP FORMS
DC.creator	Laurinčikas, Antanas
	Matsumoto, Kohji
	Steuding, Jörn
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-12
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/26828
DCTERMS.abstract	It is well-known that the zeta-function ζ(s,F) attached to a normalized Hecke-eigen cusp form F of weight κ is universal in the sense that their shifts ζ(s+iτ,F) with appropriate τ∈R approximate any analytic function uniformly on compact subsets of the strip {s=σ+it∈C:κ/2<σ<(κ+1)/2} with any prescribed accuracy. In this paper we consider some classes of operators Φ such that the function Φ(ζ(s,F)) is universal in the above sense. In particular, this implies the universality of the functions, for example, ζ(s,F)＾N (N-th power) and ζ^<(N)>(s,F) (N-th derivative) with N∈N, e^<ζ(s,F)>, sinζ(s,F), and cosζ(s,F).
DC.identifier	info:doi/10.18910/26828
citation_title	UNIVERSALITY OF SOME FUNCTIONS RELATED TO ZETA-FUNCTIONS OF CERTAIN CUSP FORMS
citation_author	Laurinčikas, Antanas
	Matsumoto, Kohji
	Steuding, Jörn
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-12
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	4
citation_firstpage	1021
citation_lastpage	1037
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/26828
citation_doi	info:doi/10.18910/26828

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