Linear dependence of quasi-periods over the rationals

K. Senthil Kumar

doi:10.5802/crmath.171

Number theory

Linear dependence of quasi-periods over the rationals

K. Senthil Kumar ¹

¹National Institute of Science Education and Research, HBNI, P.O.Jatni, Khurda, Odisha-752 050, India

Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 409-414

Abstract

In this note we shall show that a lattice $ℤ ω_{1} + ℤ ω_{2}$ in $ℂ$ has $ℚ$ -linearly dependent quasi-periods if and only if $ω_{2} / ω_{1}$ is equivalent to a zero of the Eisenstein series $E_{2}$ under the action of ${SL}_{2} (ℤ)$ on the upper half plane of $ℂ$ .

Received: 2020-03-22
Revised: 2020-08-06
Accepted: 2020-12-16
Published online: 2021-05-27

MR Zbl

DOI: 10.5802/crmath.171

Classification: 11J72, 11J89

Author's affiliations:

K. Senthil Kumar ¹

¹ National Institute of Science Education and Research, HBNI, P.O.Jatni, Khurda, Odisha-752 050, India

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Linear dependence of quasi-periods over the rationals},
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K. Senthil Kumar. Linear dependence of quasi-periods over the rationals. Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 409-414. doi: 10.5802/crmath.171

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