KRONECKER'S SOLUTION OF PELL'S EQUATION FOR CM FIELDS Academic Article

abstract

• 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.

authors

• Masri, Mohamad

published proceedings

• ANNALES DE L INSTITUT FOURIER

author list (cited authors)

• Masri, R.

citation count

• 0

complete list of authors

• Masri, Riad

publication date

• January 2013

publisher

• Cellule MathDoc/CEDRAM  Publisher

published in

• Annales de l'Institut Fourier  Journal

keywords

• Cm Point
• Hilbert Modular Function
• Pell's Equation

Digital Object Identifier (DOI)

• 10.5802/aif.2830

URI

• https://hdl.handle.net/1969.1/184478

start page

• 2287

end page

• 2306

volume

• 63

issue

• 6

URL

• http://dx.doi.org/10.5802/aif.2830