Transcendence conjectures about periods of modular forms and rational structures on spaces of modular forms

  • Winfried Kohnen

DOI: 10.1007/BF02864395

Cite this article as:
Kohnen, W. Proc. Indian Acad. Sci. (Math. Sci.) (1989) 99: 231. doi:10.1007/BF02864395


The conjecture is made that the rational structures on spaces of modular forms coming from the rationality of Fourier coefficients and the rationality of periods are not compatible. A consequence would be that ζ(2k-1)/π2k-1 (ζ(s)=Riemann zeta function;k∈ℕ,k≥2) is irrational or even transcendental.


Modular forms rational structures periods transcendence Riemann zeta function 

Copyright information

© Indian Academy of Science 1989

Authors and Affiliations

  • Winfried Kohnen
    • 1
    • 2
  1. 1.Mathematisches Institut der Universität MünsterMünsterFederal Republic of Germany
  2. 2.Max-Planck-Institut für MathematikBonn 3Federal Republic of Germany

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