In this note we shall show that a lattice in has -linearly dependent quasi-periods if and only if is equivalent to a zero of the Eisenstein series under the action of on the upper half plane of .
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.171
@article{CRMATH_2021__359_4_409_0, author = {Kumar, K. Senthil}, title = {Linear dependence of quasi-periods over the rationals}, journal = {Comptes Rendus. Math\'ematique}, pages = {409--414}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {4}, year = {2021}, doi = {10.5802/crmath.171}, mrnumber = {4264323}, zbl = {07362161}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/crmath.171/} }
TY - JOUR AU - Kumar, K. Senthil TI - Linear dependence of quasi-periods over the rationals JO - Comptes Rendus. Mathématique PY - 2021 SP - 409 EP - 414 VL - 359 IS - 4 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.171/ DO - 10.5802/crmath.171 LA - en ID - CRMATH_2021__359_4_409_0 ER -
%0 Journal Article %A Kumar, K. Senthil %T Linear dependence of quasi-periods over the rationals %J Comptes Rendus. Mathématique %D 2021 %P 409-414 %V 359 %N 4 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.171/ %R 10.5802/crmath.171 %G en %F CRMATH_2021__359_4_409_0
Kumar, K. Senthil. Linear dependence of quasi-periods over the rationals. Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 409-414. doi : 10.5802/crmath.171. http://archive.numdam.org/articles/10.5802/crmath.171/
[1] On the quasi-periods of the Weierstrass -function, Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl., Volume 1969 (1970), pp. 145-157 | Zbl
[2] The algebraic independence of Weierstrass functions and some related numbers, Acta Arith., Volume 33 (1977), pp. 111-149 | DOI | MR | Zbl
[3] Linear forms in the periods of the exponential and elliptic functions, Invent. Math., Volume 12 (1971), pp. 290-299 | DOI | MR | Zbl
[4] The transcendence of linear forms in , Am. J. Math., Volume 93 (1971), pp. 385-397 | DOI | MR | Zbl
[5] On the pseudo-periods of the Weierstrass zeta-functions, SIAM J. Numer. Anal., Volume 3 (1966), pp. 266-268 | DOI | Zbl
[6] On the pseudo-periods of the Weierstrass zeta functions. II., Nagoya Math. J., Volume 30 (1967), pp. 113-119 | DOI | MR | Zbl
[7] Elliptic functions, Graduate Texts in Mathematics, 112, Springer, 1987 | MR | Zbl
[8] Elliptic functions and transcendence, Lecture Notes in Mathematics, 437, Springer, 1975 | MR | Zbl
[9] Einführung in die transzendenten Zahlen, Grundlehren der Mathematischen Wissenschaften, 81, Springer, 1957 | MR | Zbl
[10] Über die Perioden elliptischer Funktionen, J. Reine Angew. Math., Volume 167 (1932), pp. 62-69 | Zbl
Cited by Sources: