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On Functions Satisfying Modular Equations for Infinitely Many Primes

Published online by Cambridge University Press:  20 November 2018

Dmitry N. Kozlov
Dmitry N. Kozlov*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA email: kozlov@math.ias.edu, kozlov@math.mit.edu, kozlov@math.kth.se
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Abstract

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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 ${{z}_{2}}$.

Keywords

11Mxx
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 5 , 01 October 1999 , pp. 1020 - 1034
Copyright
Copyright © Canadian Mathematical Society 1999

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