Modularity gap for Eisenstein series

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)79-84
Number of pages6
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Issue number4
Publication statusPublished - 2010 Apr


  • Eisenstein series
  • Modularity
  • Ramanujan q-series
  • Zeta functions

ASJC Scopus subject areas

  • General Mathematics


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