scholarly journals Generalized Pell numbers, balancing numbers and binary quadratic forms

2014 ◽  
Vol 23 (1) ◽  
pp. 115-122
Author(s):  
AHMET TEKCAN ◽  
◽  
MERVE TAYAT ◽  
Keyword(s):  
Quadratic Forms ◽  
Binary Quadratic Forms ◽  
Pell Numbers ◽  
Balancing Numbers

In this work, we derive some algebraic identities on generalized Pell numbers and their relationship with balancing numbers. Also we deduce some results on binary quadratic forms involving Pell and balancing numbers.

scholarly journals On S-class number relations of algebraic tori in Galois extensions of global fields

1991 ◽  
Vol 124 ◽  
pp. 133-144 ◽  
Author(s):  
Masanori Morishita
Keyword(s):  
Class Number ◽  
Quadratic Forms ◽  
Euler Number ◽  
Number Fields ◽  
Binary Quadratic Forms ◽  
Algebraic Number Fields ◽  
Algebraic Tori ◽  
Genus Theory ◽  
Class Number Formula ◽  
Number Formula

As an interpretation and a generalization of Gauss’ genus theory on binary quadratic forms in the language of arithmetic of algebraic tori, Ono [02] established an equality between a kind of “Euler number E(K/k)” for a finite Galois extension K/k of algebraic number fields and other arithmetical invariants associated to K/k. His proof depended on his Tamagawa number formula [01] and Shyr’s formula [Sh] which follows from the analytic class number formula of a torus. Later, two direct proofs were given by Katayama [K] and Sasaki [Sa].

Representing Primes by Binary Quadratic Forms

1991 ◽  
Vol 64 (1) ◽  
pp. 34
Author(s):  
Steven Galovich ◽  
Jeremy Resnick
Keyword(s):  
Quadratic Forms ◽  
Binary Quadratic Forms

scholarly journals Congruences for representations of primes by binary quadratic forms

1982 ◽  
Vol 41 (4) ◽  
pp. 311-322
Author(s):  
Richard Hudson ◽  
Kenneth Williams
Keyword(s):  
Quadratic Forms ◽  
Binary Quadratic Forms

scholarly journals Indefinite binary quadratic forms with Markov ratio exceeding 9

2003 ◽  
Vol 47 (1-2) ◽  
pp. 305-316
Author(s):  
William C. Jagy ◽  
Irving Kaplansky
Keyword(s):  
Quadratic Forms ◽  
Binary Quadratic Forms
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