Central limit theorems for sums of quadratic characters, Hecke eigenforms, and elliptic curves
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- by M. Ram Murty and Neha Prabhu PDF
- Proc. Amer. Math. Soc. 148 (2020), 965-977 Request permission
Abstract:
We prove central limit theorems (under suitable growth conditions) for sums of quadratic characters, families of Hecke eigenforms of level $1$ and weight $k$, and families of elliptic curves, twisted by an $L$-function satisfying certain properties. As a corollary, we obtain a central limit theorem for products $\chi (p)a_f(p)$ where $\chi$ is a quadratic Dirichlet character and $f$ is a normalized Hecke eigenform.References
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Additional Information
- M. Ram Murty
- Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
- MR Author ID: 128555
- Email: murty@queensu.ca
- Neha Prabhu
- Affiliation: The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, India
- MR Author ID: 1216482
- Email: nehap@imsc.res.in
- Received by editor(s): November 28, 2018
- Received by editor(s) in revised form: July 3, 2019
- Published electronically: September 20, 2019
- Additional Notes: The research of the first author is partially supported by an NSERC Discovery Grant.
The research of the second author is partially supported by a postdoctoral fellowship from The Fields Institute. - Communicated by: Amanda Folsom
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 965-977
- MSC (2010): Primary 11F30, 11N37, 11G05
- DOI: https://doi.org/10.1090/proc/14760
- MathSciNet review: 4055927