Algebraic geometry of ternary quadratic forms and orders in quaternion algebras

1981 ◽  
pp. 319-325
Author(s):  
Juliusz Brzezinski
Keyword(s):  
Algebraic Geometry ◽  
Quadratic Forms ◽  
Quaternion Algebras ◽  
Ternary Quadratic Forms

scholarly journals Ternary quadratic forms and quaternion algebras

1986 ◽  
Vol 23 (2) ◽  
pp. 203-209 ◽  
Author(s):  
Thomas R Shemanske
Keyword(s):  
Quadratic Forms ◽  
Quaternion Algebras ◽  
Ternary Quadratic Forms

scholarly journals On the representation numbers of ternary quadratic forms and modular forms of weight 3/2

2014 ◽  
Vol 140 ◽  
pp. 235-266 ◽  
Author(s):  
Xuejun Guo ◽  
Yuzhen Peng ◽  
Hourong Qin
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Ternary Quadratic Forms

FINITENESS RESULTS FOR REGULAR DEFINITE TERNARY QUADRATIC FORMS OVER ${\mathbb Q}(\sqrt{5})$

2007 ◽  
Vol 03 (04) ◽  
pp. 541-556 ◽  
Author(s):  
WAI KIU CHAN ◽  
A. G. EARNEST ◽  
MARIA INES ICAZA ◽  
JI YOUNG KIM
Keyword(s):  
Quadratic Form ◽  
Number Field ◽  
Quadratic Forms ◽  
Positive Definite ◽  
Integral Quadratic Form ◽  
Ring Of Integers ◽  
Ternary Quadratic Forms ◽  
Totally Positive ◽  
Finiteness Result

Let 𝔬 be the ring of integers in a number field. An integral quadratic form over 𝔬 is called regular if it represents all integers in 𝔬 that are represented by its genus. In [13,14] Watson proved that there are only finitely many inequivalent positive definite primitive integral regular ternary quadratic forms over ℤ. In this paper, we generalize Watson's result to totally positive regular ternary quadratic forms over [Formula: see text]. We also show that the same finiteness result holds for totally positive definite spinor regular ternary quadratic forms over [Formula: see text], and thus extends the corresponding finiteness results for spinor regular quadratic forms over ℤ obtained in [1,3].

Ternary Quadratic Forms and Eta Quotients

2015 ◽  
Vol 58 (4) ◽  
pp. 858-868 ◽  
Author(s):  
Kenneth S. Williams
Keyword(s):  
Quadratic Forms ◽  
Fourier Coefficients ◽  
Arithmetic Progressions ◽  
Dedekind Eta Function ◽  
Ternary Quadratic Forms ◽  
Sum Formula ◽  
Image Position ◽  
Positive Integers

AbstractLet denote the Dedekind eta function. We use a recent productto- sum formula in conjunction with conditions for the non-representability of integers by certain ternary quadratic forms to give explicitly ten eta quotientssuch that the Fourier coefficients c(n) vanish for all positive integers n in each of infinitely many non-overlapping arithmetic progressions. For example, we show that if we have c(n) = 0 for all n in each of the arithmetic progressions

Sign in / Sign up

Export Citation Format

Share Document