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

Abstract

It is proved that for all but a finite set of the square-free integers $d$ the value of transcendental function $\exp (2\pi ix+\log \log y)$ 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 $-d$.

to appear Ramanujan J

References in corpus (1)

• On a symmetry of complex and real multiplication

Cited by in corpus (2)

• Non-abelian class field theory and higher dimensional noncommutative tori
• Quantum arithmetic of Drinfeld modules