scholarly journals The Equivalence of Quadratic Forms

1957 ◽  
Vol 9 ◽  
pp. 526-548 ◽  
Author(s):  
G. L. Watson
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic ◽  
Number Of Classes

The main object of this paper is to find the number of classes in a genus of indefinite quadratic forms, with integral coefficients, in k ≥ 4 variables, distinguishing for even k two cases, according as improper equivalence is or is not admitted.

scholarly journals Strongly indefinite quadratic forms and wild algebras

1990 ◽  
Vol 26 (1) ◽  
pp. 341-351
Author(s):  
Nikolaos Marmaridis
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic

scholarly journals Quadratic ideals, indefinite quadratic forms and some specific diophantine equations

2018 ◽  
Vol 36 (3) ◽  
pp. 173-192
Author(s):  
Ahmet Tekcan ◽  
Seyma Kutlu
Keyword(s):  
Diophantine Equation ◽  
Quadratic Forms ◽  
Diophantine Equations ◽  
Algebraic Properties ◽  
Integer Solutions ◽  
Indefinite Quadratic

Let $k\geq 1$ be an integer and let $P=k+2,Q=k$ and $D=k^{2}+4$. In this paper, we derived some algebraic properties of quadratic ideals $I_{\gamma}$ and indefinite quadratic forms $F_{\gamma }$ for quadratic irrationals $\gamma$, and then we determine the set of all integer solutions of the Diophantine equation $F_{\gamma }^{\pm k}(x,y)=\pm Q$.

scholarly journals On indefinite quadratic forms

1977 ◽  
Vol 29 (2) ◽  
pp. 355-361 ◽  
Author(s):  
Tsuneo TAMAGAWA
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic

scholarly journals On some class number relations for Galois extensions

1987 ◽  
Vol 107 ◽  
pp. 121-133 ◽  
Author(s):  
Takashi Ono
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Class Number ◽  
Quadratic Forms ◽  
Algebraic Number Field ◽  
Narrow Sense ◽  
Binary Quadratic Forms ◽  
Finite Degree ◽  
Algebraic Tori ◽  
Number Of Classes

Let k be an algebraic number field of finite degree over Q, the field of rationals, and K be an extension of finite degree over k. By the use of the class number of algebraic tori, we can introduce an arithmetical invariant E(K/k) for the extension K/k. When k = Q and K is quadratic over Q, the formula of Gauss on the genera of binary quadratic forms, i.e. the formula where = the class number of K in the narrow sense, the number of classes is a genus of the norm form of K/Q and tK = the number of distinct prime factors of the discriminant of K, may be considered as an equality between E(K/Q) and other arithmetical invariants of K.

Indefinite Quadratic Forms

1959 ◽  
Vol s3-9 (4) ◽  
pp. 544-555 ◽  
Author(s):  
H. Davenport ◽  
D. Ridout
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic
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