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On Functions Satisfying Modular Equations for Infinitely Many Primes
Dmitry N. Kozlov
Journal:

Canadian Journal of Mathematics / Volume 51 / Issue 5 / 01 October 1999

Published online by Cambridge University Press:

20 November 2018, pp. 1020-1034

Print publication:

01 October 1999
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In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are:
1. 1) every such function is analytic in the upper half plane;
2. 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 ${{z}_{2}}$.