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mathematics

Algebraic results for the values ϑ3(Mτ) and ϑ3(nτ) of the jacobi theta-constant

Moscow Journal of Combinatorics and Number Theory, Volume 8, No. 1, Year 2019

Let ϑ3(τ) = 1 + 2∑∞ ν=1eπiν2τ denote the classical Jacobi theta-constant. We prove that the two values ϑ3(mτ) and ϑ3(nτ) are algebraically independent over Q for any τ in the upper half-plane such that q = eπiτ is an algebraic number, where m, n ≥ 2 are distinct integers.

Statistics
Citations: 4
Authors: 3
Affiliations: 5
Identifiers
Doi: 10.2140/moscow.2019.8.71
ISSN: 22205438
e-ISSN: 26407361

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