ON CRITERIA FOR UNIVERSALITY OF TERNARY QUADRATIC FORMS

1933 ◽  
Vol os-4 (1) ◽  
pp. 147-158 ◽  
Author(s):  
ARNOLD E. ROSS
Keyword(s):  
Quadratic Forms ◽  
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

On the existence of integral ternary quadratic forms without automorphs of finite order

2017 ◽  
Vol 26 (14) ◽  
pp. 1750102 ◽  
Author(s):  
José María Montesinos-Amilibia
Keyword(s):  
Quadratic Form ◽  
Finite Order ◽  
Quadratic Forms ◽  
Ternary Quadratic Form ◽  
Ternary Quadratic Forms

An example of an integral ternary quadratic form [Formula: see text] such that its associated orbifold [Formula: see text] is a manifold is given. Hence, the title is proved.

The number of representations of integers by generalized Bell ternary quadratic forms

2020 ◽  
pp. 1-15
Author(s):  
Kyoungmin Kim ◽  
Yeong-Wook Kwon
Keyword(s):  
Quadratic Form ◽  
Class Number ◽  
Quadratic Forms ◽  
Positive Definite ◽  
Cusp Forms ◽  
Ternary Quadratic Form ◽  
Closed Formula ◽  
Integral Quadratic Form ◽  
Ternary Quadratic Forms ◽  
Representations Of Integers

For a positive definite ternary integral quadratic form [Formula: see text], let [Formula: see text] be the number of representations of an integer [Formula: see text] by [Formula: see text]. A ternary quadratic form [Formula: see text] is said to be a generalized Bell ternary quadratic form if [Formula: see text] is isometric to [Formula: see text] for some nonnegative integers [Formula: see text]. In this paper, we give a closed formula for [Formula: see text] for a generalized Bell ternary quadratic form [Formula: see text] with [Formula: see text] and class number greater than [Formula: see text] by using the Minkowski–Siegel formula and bases for spaces of cusp forms of weight [Formula: see text] and level [Formula: see text] with [Formula: see text] consisting of eta-quotients.

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