The basis problem for modular forms for the Weil representation

2024/07/01 by Müller, Manuel K. -H. · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.01205

Abstract

The vector valued theta series of a positive-definite even lattice is a modular form for the Weil representation of SL₂(ℤ). We show that the space of cusp forms for the Weil representation is generated by such functions. This gives a positive answer to Eichler's basis problem in this case. As applications we derive Waldspurger's result on the basis problem for scalar valued modular forms and give a new proof of the surjectivity of the Borcherds lift based on the analysis of local Picard groups.

Cited by

• A new converse theorem for Borcherds products
• Hermitian modular forms and algebraic modular forms on SO(6)

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