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Dal'nevost. Mat. Zh., 2016, Volume 16, Number 2, Pages 181–185 (Mi dvmg332)  

On the rank of a finite set of theta functions

M. D. Monina

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Abstract: In the work for the theta function
$$ \theta(z)=\theta(z;q)=\sum\limits_{n=-\infty}^{\infty}e^{2izn}q^{n^2} $$
identity
\begin{gather*} \theta(z_1+w)…\theta(z_{k-1}+w)\theta(z_1+…+z_{k-1}-w)=\sum\limits_{i=1}^{s}\varphi_i(z_1,…,z_{k-1})\psi_i(w)
(\forall z_1,…, z_{k-1}, w \in \mathbb{C}) \end{gather*}
with some clearly indicates theta functions $\psi_i$ of one variable and functions $\varphi_i$ of $k-1$ variables is proved.

Key words: theta function, elliptic function, Weierstrass sigma-function.

Funding Agency Grant Number
Far Eastern Branch of the Russian Academy of Sciences 15-I-4-047
Russian Foundation for Basic Research 14-01-00203 a
Government of Khabarovsk Territory 479-РП


Full text: PDF file (91 kB)
References: PDF file   HTML file
UDC: 517.965+517.547.582
MSC: 33E05
Received: 10.10.2016

Citation: M. D. Monina, “On the rank of a finite set of theta functions”, Dal'nevost. Mat. Zh., 16:2 (2016), 181–185

Citation in format AMSBIB
\Bibitem{Mon16}
\by M.~D.~Monina
\paper On the rank of a finite set of theta functions
\jour Dal'nevost. Mat. Zh.
\yr 2016
\vol 16
\issue 2
\pages 181--185
\mathnet{http://mi.mathnet.ru/dvmg332}
\elib{https://elibrary.ru/item.asp?id=27701002}


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