Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Central limit theorems for sums of quadratic characters, Hecke eigenforms, and elliptic curves


Authors: M. Ram Murty and Neha Prabhu
Journal: Proc. Amer. Math. Soc. 148 (2020), 965-977
MSC (2010): Primary 11F30, 11N37, 11G05
DOI: https://doi.org/10.1090/proc/14760
Published electronically: September 20, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11F30, 11N37, 11G05

Retrieve articles in all journals with MSC (2010): 11F30, 11N37, 11G05


Additional Information

M. Ram Murty
Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
Email: murty@queensu.ca

Neha Prabhu
Affiliation: The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, India
Email: nehap@imsc.res.in

DOI: https://doi.org/10.1090/proc/14760
Keywords: Central limit theorem, elliptic curves, quadratic characters, modular forms
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
Article copyright: © Copyright 2019 American Mathematical Society