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arXiv · 1210.4747

On algebraic values of function exp (2ni x + log log y)

Igor Nikolaev
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Abstract

It is proved that for all but a finite set of the square-free integers $d$ the value of transcendental function $\exp~(2πi ~x+\log\log y)$ 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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Igor Nikolaev. 2017-10-26. On algebraic values of function exp (2ni x + log log y). https://doi.org/10.1007/s11139-017-9969-3

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