Proceedings of the Japan Academy, Series A, Mathematical Sciences

Modularity gap for Eisenstein series

Shun Shimomura

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

First available in Project Euclid: 1 April 2010

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Zentralblatt MATH identifier

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

Eisenstein series modularity zeta functions Ramanujan q-series


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.

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