Probabilities as values of modular forms and continued fractions.
The distribution of zeros of Epstein zeta functions over GLₙ
Kronecker’s solution of Pell’s equation for CM fields
We generalize Kronecker’s solution of Pell’s equation to CM fields whose Galois group over is an elementary abelian 2-group. This is an identity which relates CM values of a certain Hilbert modular function to products of logarithms of fundamental units. When is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of . Assuming Schanuel’s conjecture, we show that when has degree greater than 2 over these CM values are transcendental....
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