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Currently displaying 1 – 3 of 3

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Probabilities as values of modular forms and continued fractions.

Masri, Riad; Ono, Ken — 2009

International Journal of Mathematics and Mathematical Sciences

The distribution of zeros of Epstein zeta functions over GLₙ

Riad Masri — 2007

Acta Arithmetica

Kronecker’s solution of Pell’s equation for CM fields

Riad Masri — 2013

Annales de l’institut Fourier

We generalize Kronecker’s solution of Pell’s equation to CM fields $K$ whose Galois group over $ℚ$ 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 $K$ is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of $K$ . Assuming Schanuel’s conjecture, we show that when $K$ has degree greater than 2 over $ℚ$ these CM values are transcendental....

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