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, \(-d\).
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Nikolaev, I. On algebraic values of function \(\exp ~(2\pi i ~x+\log \log y)\) . Ramanujan J 47, 417–425 (2018). https://doi.org/10.1007/s11139-017-9969-3
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DOI: https://doi.org/10.1007/s11139-017-9969-3