scholarly journals Computing the rank of elliptic curves over real quadratic number fields of class number 1

1999 ◽  
Vol 68 (227) ◽  
pp. 1187-1201 ◽  
Author(s):  
J. E. Cremona ◽  
P. Serf
Keyword(s):  
Elliptic Curves ◽  
Class Number ◽  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Real Quadratic

scholarly journals On a class of insoluble binary quadratic diophantine equations

1991 ◽  
Vol 123 ◽  
pp. 141-151 ◽  
Author(s):  
Franz Halter-Koch
Keyword(s):  
Diophantine Equation ◽  
Class Number ◽  
Diophantine Equations ◽  
Number Fields ◽  
Quadratic Number ◽  
Number Problem ◽  
Quadratic Number Fields ◽  
Quadratic Diophantine Equation ◽  
Real Quadratic

The binary quadratic diophantine equationis of interest in the class number problem for real quadratic number fields and was studied in recent years by several authors (see [4], [5], [2] and the literature cited there).

scholarly journals On a class number formula for real quadratic number fields

2002 ◽  
Vol 65 (2) ◽  
pp. 259-270 ◽  
Author(s):  
David M. Bradley ◽  
Ali E. Özlük ◽  
C. Snyder
Keyword(s):  
Class Number ◽  
Dirichlet Character ◽  
Number Fields ◽  
Binomial Coefficients ◽  
Quadratic Number ◽  
Numerical Series ◽  
Class Number Formula ◽  
Quadratic Number Fields ◽  
Number Formula ◽  
Real Quadratic

For an even Dirichlet character ψ, we obtain a formula for L (1, ψ) in terms of a sum of Dirichlet L-Series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coefficients. We then derive a class number formula for real quadratic number fields by taking L (s, ψ) to be the quadratic L-series associated with these fields.

The Class-Number of Real Quadratic Number Fields

1952 ◽  
Vol 56 (3) ◽  
pp. 479 ◽  
Author(s):  
N. C. Ankeny ◽  
E. Artin ◽  
S. Chowla
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Real Quadratic
Sign in / Sign up

Export Citation Format

Share Document