A converse theorem for quasimodular forms
-
Mrityunjoy Charan
and
Ranveer Kumar Singh
Abstract
In this paper, we consider twisted Dirichlet series attached to quasimodular forms, study their analytic properties, and prove an analogue of Weil’s converse theorem for quasimodular forms over congruence subgroups. We also give some applications of our results to a certain q-series and sign changes of the Fourier coefficients of quasimodular forms.
Funding source: Science and Engineering Research Board
Award Identifier / Grant number: CRG/2020/004147
Funding statement: The research of the second author was partially supported by the DST-SERB, grant number CRG/2020/004147.
Acknowledgements
We would like to thank the referee for his careful reading and some useful comments which improved the presentation of the article.
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Articles in the same Issue
- Frontmatter
- On the variance of the nodal volume of arithmetic random waves
- On length densities
- On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
- Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
- On cutting blocking sets and their codes
- Inertia groups and smooth structures on quaternionic projective spaces
- On the number of zeros of diagonal quartic forms over finite fields
- Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
- A dual version of Huppert's ρ-σ conjecture for character codegrees
- A topological correspondence between partial actions of groups and inverse semigroup actions
- On homotopy braids
- Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf
- The Shintani double zeta functions
- Homological dimensions relative to preresolving subcategories II
- Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
- A converse theorem for quasimodular forms
