Proceedings of the Japan Academy, Series A, Mathematical Sciences

Modularity gap for Eisenstein series

Shun Shimomura

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 86, Number 4 (2010), 79-84.

Dates
First available in Project Euclid: 1 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.pja/1270127451

Digital Object Identifier
doi:10.3792/pjaa.86.79

Mathematical Reviews number (MathSciNet)
MR2657331

Zentralblatt MATH identifier
1214.11098

Subjects
Primary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
Secondary: 30B30: Boundary behavior of power series, over-convergence

Keywords
Eisenstein series modularity zeta functions Ramanujan q-series

Citation

Shimomura, Shun. Modularity gap for Eisenstein series. Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 4, 79--84. doi:10.3792/pjaa.86.79. https://projecteuclid.org/euclid.pja/1270127451


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References

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