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The Ramanujan Journal

, Volume 47, Issue 2, pp 417–425 | Cite as

On algebraic values of function \(\exp ~(2\pi i ~x+\log \log y)\)

  • Igor Nikolaev
Article
  • 87 Downloads

Abstract

It is proved that, for all but a finite set of the square-free integers, d the value of transcendental function \(\exp ~(2\pi i ~x+\log \log y)\) is an algebraic number for the algebraic arguments x and y lying in a real quadratic field of discriminant, d. Such a value generates the Hilbert class field of the imaginary quadratic field of discriminant, \(-d\).

Keywords

Real multiplication Sklyanin algebra Noncommutative tori 

Mathematics Subject Classification

11J81 (transcendence theory) 46L85 (noncommutative topology) 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceSt. John’s UniversityNew YorkUSA

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