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Zeros of Eisenstein series; zeros of modular forms of $\Gamma_{0}(N)$.

This paper provides a simple method to extract the zeros of some weight two Eisenstein series of level $N$ where $N$ = 2, 3, 5 and 7. The method is based on the observation that these Eisenstein series are integral over the graded algebra of modular forms on $SL(2, Z)$ and their zeros are ‘controlled’ by those of $E_{4}$ and $E_{6}$ in the fundamental domain of $\Gamma_{0}(N)$.

ARADHITA CHATTOPADHYAYA¹

1. Department of Centre for High Energy Physics, Indian Institute of Science, Bangalore 560 012, India

Published

10 January 2020

Manuscript received

11 March 2019

Manuscript revised

15 June 2019

Accepted

22 June 2019

Early published

Unedited version published online

Final version published online

9 January 2020