scholarly journals ON THETA FUNCTIONS OF BINARY QUADRATIC FORMS WITH CONGRUENCE CONDITION

2021 ◽  
Vol 75 (1) ◽  
pp. 41-54
Author(s):  
Masanari KIDA ◽  
Ryota OKANO ◽  
Ken YOKOYAMA
Keyword(s):  
Quadratic Forms ◽  
Theta Functions ◽  
Congruence Condition ◽  
Binary Quadratic Forms

scholarly journals Vector valued theta functions associated with binary quadratic forms

2016 ◽  
Vol 28 (5) ◽  
pp. 893-908 ◽  
Author(s):  
Stephan Ehlen
Keyword(s):  
Quadratic Forms ◽  
Theta Functions ◽  
Positive Definite ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Binary Quadratic Forms ◽  
Fundamental Discriminant ◽  
Weight One ◽  
Petersson Norms ◽  
Vector Valued

AbstractWe study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta functions of weight one and determine an orthogonal basis with respect to the Petersson inner product. Moreover, we give an explicit formula for the Petersson norms of the elements of this basis.

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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