Modularity gap for Eisenstein series

Shun Shimomura

doi:10.3792/pjaa.86.79

Modularity gap for Eisenstein series

Shun Shimomura

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	79-84
Number of pages	6
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	86
Issue number	4
DOIs	https://doi.org/10.3792/pjaa.86.79
Publication status	Published - 2010 Apr
Externally published	Yes

Keywords

Eisenstein series
Modularity
Ramanujan q-series
Zeta functions

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.3792/pjaa.86.79

Cite this

@article{f7a47f7c9727449dbd046555aec6b8db,

title = "Modularity gap for Eisenstein series",

abstract = "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.",

keywords = "Eisenstein series, Modularity, Ramanujan q-series, Zeta functions",

author = "Shun Shimomura",

year = "2010",

month = apr,

doi = "10.3792/pjaa.86.79",

language = "English",

volume = "86",

pages = "79--84",

journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",

issn = "0386-2194",

publisher = "Japan Academy",

number = "4",

}

TY - JOUR

T1 - Modularity gap for Eisenstein series

AU - Shimomura, Shun

PY - 2010/4

Y1 - 2010/4

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=77953665390&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953665390&partnerID=8YFLogxK

U2 - 10.3792/pjaa.86.79

DO - 10.3792/pjaa.86.79

M3 - Article

AN - SCOPUS:77953665390

SN - 0386-2194

VL - 86

SP - 79

EP - 84

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

IS - 4

ER -

Modularity gap for Eisenstein series

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this