Coprimality of Fourier coefficients of eigenforms

Satadal Ganguly; Arvind Kumar; Moni Kumari

doi:10.4064/aa210817-8-2

Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

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Coprimality of Fourier coefficients of eigenforms

Volume 203 / 2022

Satadal Ganguly, Arvind Kumar, Moni Kumari Acta Arithmetica 203 (2022), 69-96 MSC: Primary 11F30; Secondary 11F80, 11N37, 11N64, 11N99. DOI: 10.4064/aa210817-8-2 Published online: 24 March 2022

Abstract

Given a pair of distinct non-CM normalized eigenforms having integer Fourier coefficients $a_1 (n)$ and $a_2(n)$ , we count positive integers $n$ with $(a_1(n), a_2(n))=1$ and make a conjecture about the density of the set of primes $p$ for which $(a_1(p), a_2(p))=1$ . We also study the average order of the number of prime divisors of $(a_1(p), a_2(p))$ .

Authors

Satadal GangulyTheoretical Statistics and Mathematics Unit
Indian Statistical Institute
203 Barrackpore Trunk Road
Kolkata 700108, India
e-mail
Arvind KumarEinstein Institute of Mathematics
The Hebrew University of Jerusalem
Edmund Safra Campus
Jerusalem 91904, Israel
e-mail
Moni KumariDepartment of Mathematics
Bar-Ilan University
Ramat Gan 52900, Israel
e-mail

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Institute of Mathematics / Publishing house / Journals and Serials / Acta Arithmetica / All issues

Acta Arithmetica

Coprimality of Fourier coefficients of eigenforms

Volume 203 / 2022

Abstract

Authors

Search for IMPAN publications

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