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On Functions Satisfying Modular Equations for Infinitely Many Primes
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are:
1) every such function is analytic in the upper half plane;
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 ${{z}_{2}}$.
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- Research Article
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- Copyright © Canadian Mathematical Society 1999
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