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# On Functions Satisfying Modular Equations for Infinitely Many Primes

Published:1999-10-01
Printed: Oct 1999
• Dmitry N. Kozlov
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## Abstract

In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are: \begin{enumerate} \item[1)] every such function is analytic in the upper half plane; \item[2)] if such function takes the same value in two different points $z_1$ and $z_2$ then there exists an $f$-preserving analytic bijection between neighbourhoods of $z_1$ and $z_2$. \end{enumerate}
 MSC Classifications: 11Mxx - Zeta and $L$-functions: analytic theory