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

Riad Masri

Type: Article

Publication Date: 2013-01-01

Citations: 0

DOI: https://doi.org/10.5802/aif.2830

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.

Locations

OAKTRUST (Texas A&M University) - View - PDF
French digital mathematics library (Numdam) - View - PDF
Annales de l’institut Fourier - View - PDF

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+	Lectures on advanced analytic number theory	1961	Carl Ludwig Siegel S. Raghavan
+	Intersections of Hirzebruch–Zagier Divisors and CM Cycles	2012	Benjamin Howard Tonghai Yang
+ PDF Chat	Transcendental values of class group $L$-functions, II	2012	M. Ram Murty V. Kumar Murty
+ PDF Chat	On Kronecker's limit formula in a totally imaginary quadratic field over a totally real algebraic number field	1965	Shuji Konno
+	CM-values of Hilbert modular functions	2005	Jan Hendrik Bruinier Tonghai Yang
+	Transcendence of Values of Class Group L-Functions	2014	M. Ram Murty V. Kumar Murty
+	On the Imaginary Bicyclic Biquadratic Fields With Class-Number 2	1977	D. A. Buell H. C. Williams K. S. Williams
+	Transcendental values of class group L-functions	2010	M. Ram Murty V. Kumar Murty
+	Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables	2010	Michel Waldschmidt