Poincaré and Eisenstein series for Jacobi forms of lattice index

2017/12/21 by Mocanu, Andreea · 2 citations
#11F30 #11F50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1712.08174

Abstract

Poincaré and Eisenstein series are building blocks for every type of modular forms. We define Poincaré series for Jacobi forms of lattice index and state some of their basic properties. We compute the Fourier expansions of Poincaré and Eisenstein series and give an explicit formula for the Fourier coefficients of the trivial Eisenstein series. For even weight and fixed index, finite linear combinations of Fourier coefficients of non-trivial Eisenstein series are equal to finite linear combinations of Fourier coefficients of the trivial one.

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• Isomorphism between Jacobi forms of index D_2n+1 and elliptic modular forms of level 2
• Rational K3 Homotopy and the Largest Mathieu Group

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