Petersson inner products of weight-one modular forms
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Maryna Viazovska
Abstract
In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that these Petersson products posses remarkable arithmetic properties. Namely, such a Petersson product is equal to the logarithm of a certain algebraic number lying in a ring class field associated to the binary quadratic form. A similar result was obtained independently using a different method by W. Duke and Y. Li [5]. The main result of this paper is an explicit factorization formula for the algebraic number obtained by exponentiating a Petersson product.
Acknowledgements
I thank D. Zagier for introducing me to the subject and for his valuable comments on the manuscript. I thank W. Duke, S. Ehlen and Y. Li for fruitful discussions. Also I would like to thank Max Planck Institute for Mathematics and Institut des Hautes Études Scientifiques for their hospitality and for excellent working conditions.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Modulo p parabolic induction of pro-p-Iwahori Hecke algebra
- There are genus one curves of every index over every infinite, finitely generated field
- Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle
- Petersson inner products of weight-one modular forms
- Severi varieties and Brill–Noether theory of curves on abelian surfaces
- Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
- Semi-continuity of stability for sheaves and variation of Gieseker moduli spaces
- Improved bounds in Weaver and Feichtinger conjectures
- On the ramification of étale cohomology groups
Artikel in diesem Heft
- Frontmatter
- Modulo p parabolic induction of pro-p-Iwahori Hecke algebra
- There are genus one curves of every index over every infinite, finitely generated field
- Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle
- Petersson inner products of weight-one modular forms
- Severi varieties and Brill–Noether theory of curves on abelian surfaces
- Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
- Semi-continuity of stability for sheaves and variation of Gieseker moduli spaces
- Improved bounds in Weaver and Feichtinger conjectures
- On the ramification of étale cohomology groups
