New York Journal of Mathematics
Volume 30 (2024), 521-531


Hui Xue

Linear independence between odd and even periods of modular forms

view    print

Published: March 31, 2024.
Keywords: Eisenstein series, Rankin's identity, linear independence, periods of modular forms.
Subject [2010]: 11F67,11F30.

We investigate the linear dependence between an odd period and an even period of modular forms. We show that two periods of different parity are linearly independent provided that the even period has index at least 6 or the odd period has index at least 7.


The author is grateful to the referee for careful reading of the paper and valuable suggestions and comments.

Author information

Hui Xue
School of Mathematical and Statistical Sciences
Clemson University
Clemson, SC 29634-0975, USA