Open Access
April 2010 Modularity gap for Eisenstein series
Shun Shimomura
Proc. Japan Acad. Ser. A Math. Sci. 86(4): 79-84 (April 2010). DOI: 10.3792/pjaa.86.79


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.


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Shun Shimomura. "Modularity gap for Eisenstein series." Proc. Japan Acad. Ser. A Math. Sci. 86 (4) 79 - 84, April 2010.


Published: April 2010
First available in Project Euclid: 1 April 2010

zbMATH: 1214.11098
MathSciNet: MR2657331
Digital Object Identifier: 10.3792/pjaa.86.79

Primary: 11M36
Secondary: 30B30

Keywords: Eisenstein series , modularity , Ramanujan q-series , zeta functions

Rights: Copyright © 2010 The Japan Academy

Vol.86 • No. 4 • April 2010
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