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Algebraic results
for the values $\vartheta_3(m\tau)$ and $\vartheta_3(n\tau)$
of the Jacobi theta-constant
Carsten Elsner, Florian Luca and Yohei Tachiya |
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Vol. 8 (2019), No. 1, 71–79
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DOI: 10.2140/moscow.2019.8.71
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Abstract |
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Let denote the classical Jacobi theta-constant. We prove that the two values and are algebraically independent over for any in the upper half-plane such that is an algebraic number, where are distinct integers. |
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Keywords
algebraic independence, Jacobi theta-constants, modular
functions
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Mathematical Subject Classification 2010
Primary: 11J85
Secondary: 11J91, 11F27
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Milestones
Received: 10 January 2018
Revised: 18 June 2018
Accepted: 3 July 2018
Published: 11 August 2018
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Authors |
| Carsten Elsner | ||
| Fachhochschule für die
Wirtschaft University of Applied Sciences Hannover Germany |
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| Florian Luca | ||
| School of Mathematics University of the Witwatersrand Johannesburg South Africa |
Max Planck Mathematical
Institute Bonn Germany |
Department of Mathematics Faculty of Sciences University of Ostrava Ostrava Czech Republic |
| Yohei Tachiya | ||
| Graduate School of Science and
Technology Hirosaki University Hirosaki Japan |
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