Cycle integrals of meromorphic modular forms and Siegel theta functions
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Date
2024-07
Publication Type
Journal Article
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yes
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Abstract
We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the modular curve. We show that suitable linear combinations of these meromorphic modular forms have rational cycle integrals. Along the way we evaluate the cycle integrals of the Siegel theta function associated with an even lattice of signature (1, 2) in terms of Hecke's indefinite theta functions.
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published
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Volume
64 (3)
Pages / Article No.
765 - 777
Publisher
Springer
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Software
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Subject
Meromorphic modular forms; Geodesic cycle integrals; Theta functions; Theta liftings
Organisational unit
08799 - Imamoglu, Oezlem (Tit.-Prof.)