Euclidean real quadratic number fields

1985 ◽  
Vol 44 (4) ◽  
pp. 340-347 ◽  
Author(s):  
David H. Johnson ◽  
Clifford S. Queen ◽  
Alicia N. Sevilla
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Real Quadratic

The narrow 2-class field tower of some real quadratic number fields

2020 ◽  
Vol 194 (2) ◽  
pp. 187-217
Author(s):  
Elliot Benjamin ◽  
C. Snyder
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Class Field ◽  
Quadratic Number Fields ◽  
Class Field Tower ◽  
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 θ-congruent numbers on real quadratic number fields

2015 ◽  
Vol 38 (2) ◽  
pp. 352-364 ◽  
Author(s):  
Ali S. Janfada ◽  
Sajad Salami
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Real Quadratic

scholarly journals Sums of Kloosterman sums for real quadratic number fields

2003 ◽  
Vol 99 (1) ◽  
pp. 90-119
Author(s):  
R.W. Bruggeman ◽  
R.J. Miatello ◽  
I. Pacharoni
Keyword(s):  
Number Fields ◽  
Kloosterman Sums ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Real Quadratic

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.

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