Kronecker’s solution of Pell’s equation for CM fields
Riad Masri[1]
- [1] Texas A&M University Department of Mathematics College Station, TX 77843 (USA)
Annales de l’institut Fourier (2013)
- Volume: 63, Issue: 6, page 2287-2306
- ISSN: 0373-0956
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topMasri, Riad. "Kronecker’s solution of Pell’s equation for CM fields." Annales de l’institut Fourier 63.6 (2013): 2287-2306. <http://eudml.org/doc/275625>.
@article{Masri2013,
abstract = {We generalize Kronecker’s solution of Pell’s equation to CM fields $K$ whose Galois group over $\mathbb\{Q\}$ 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 $\mathbb\{Q\}$ these CM values are transcendental.},
affiliation = {Texas A&M University Department of Mathematics College Station, TX 77843 (USA)},
author = {Masri, Riad},
journal = {Annales de l’institut Fourier},
keywords = {CM point; Hilbert modular function; Pell’s equation; Pell's equation},
language = {eng},
number = {6},
pages = {2287-2306},
publisher = {Association des Annales de l’institut Fourier},
title = {Kronecker’s solution of Pell’s equation for CM fields},
url = {http://eudml.org/doc/275625},
volume = {63},
year = {2013},
}
TY - JOUR
AU - Masri, Riad
TI - Kronecker’s solution of Pell’s equation for CM fields
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 6
SP - 2287
EP - 2306
AB - We generalize Kronecker’s solution of Pell’s equation to CM fields $K$ whose Galois group over $\mathbb{Q}$ 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 $\mathbb{Q}$ these CM values are transcendental.
LA - eng
KW - CM point; Hilbert modular function; Pell’s equation; Pell's equation
UR - http://eudml.org/doc/275625
ER -
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