Linear dependence of quasi-periods over the rationals

Kumar, K. Senthil

doi:10.5802/crmath.171

Théorie des nombres

Linear dependence of quasi-periods over the rationals

Kumar, K. Senthil ¹

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

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

Résumé

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 $ℂ$ .

Reçu le : 2020-03-23
Révisé le : 2020-08-07
Accepté le : 2020-12-17
Publié le : 2021-05-27

MR Zbl

DOI : 10.5802/crmath.171

Classification : 11J72, 11J89

Affiliations des auteurs :

Kumar, K. Senthil ¹

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

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

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