Modularity gap for Eisenstein series

Shun Shimomura

doi:10.3792/pjaa.86.79

Modularity gap for Eisenstein series

Shun Shimomura

数理科学科

研究成果: Article › 査読

1 被引用数 (Scopus)

抄録

We present a formula describing modularity gap for Eisenstein series, which is written in terms of a certain double series. Limit values of the gap at nonzero rational points are expressible by Hurwitz zeta values. Our gap estimates near the origin are applied to examining the asymptotic behaviour of Ramanujan q-series and q-zeta values near the natural boundary |q| = 1.

本文言語	English
ページ（範囲）	79-84
ページ数	6
ジャーナル	Proceedings of the Japan Academy Series A: Mathematical Sciences
巻	86
号	4
DOI	https://doi.org/10.3792/pjaa.86.79
出版ステータス	Published - 2010 4

ASJC Scopus subject areas

Mathematics(all)

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10.3792/pjaa.86.79

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引用スタイル

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AB - We present a formula describing modularity gap for Eisenstein series, which is written in terms of a certain double series. Limit values of the gap at nonzero rational points are expressible by Hurwitz zeta values. Our gap estimates near the origin are applied to examining the asymptotic behaviour of Ramanujan q-series and q-zeta values near the natural boundary |q| = 1.

KW - Eisenstein series

KW - Modularity

KW - Ramanujan q-series

KW - Zeta functions

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