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Licensed Unlicensed Requires Authentication Published by De Gruyter December 19, 2019

Congruences in Hermitian Jacobi and Hermitian modular forms

  • Jaban Meher EMAIL logo and Sujeet Kumar Singh
From the journal Forum Mathematicum

Abstract

In this paper, we first prove an isomorphism between certain spaces of Jacobi forms. Using this isomorphism, we study the mod p theory of Hermitian Jacobi forms over (i). We then apply the mod p theory of Hermitian Jacobi forms to characterize U(p) congruences and to study Ramanujan-type congruences for Hermitian Jacobi forms and Hermitian modular forms of degree 2 over (i).

MSC 2010: 11F33; 11F55; 11F50

Communicated by Jan Bruinier


Award Identifier / Grant number: MTR/2017/000022

Funding statement: The research of the first author was partially supported by the DST-SERB grant MTR/2017/000022.

Acknowledgements

We have used the open source mathematics software SAGE to do our computations. The authors would like to thank Dr. Soumya Das for his valuable suggestions.

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Received: 2019-09-05
Revised: 2019-11-12
Published Online: 2019-12-19
Published in Print: 2020-03-01

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