scholarly journals Class numbers and representations by ternary quadratic forms with congruence conditions

2021 ◽  
pp. 1
Author(s):  
Kathrin Bringmann ◽  
Ben Kane
Keyword(s):  
Quadratic Forms ◽  
Class Numbers ◽  
Ternary Quadratic Forms

scholarly journals Class numbers of ternary quadratic forms

2014 ◽  
Vol 135 ◽  
pp. 221-261 ◽  
Author(s):  
Wai Kiu Chan ◽  
Byeong-Kweon Oh
Keyword(s):  
Quadratic Forms ◽  
Class Numbers ◽  
Ternary Quadratic Forms

Ternary quadratic forms and the class numbers of imaginary quadratic fields

2019 ◽  
Vol 47 (11) ◽  
pp. 4605-4640
Author(s):  
Lei Gao ◽  
Hourong Qin
Keyword(s):  
Quadratic Forms ◽  
Quadratic Fields ◽  
Class Numbers ◽  
Imaginary Quadratic Fields ◽  
Ternary Quadratic Forms

scholarly journals Class numbers of indefinite binary quadratic forms

1982 ◽  
Vol 15 (2) ◽  
pp. 229-247 ◽  
Author(s):  
Peter Sarnak
Keyword(s):  
Quadratic Forms ◽  
Class Numbers ◽  
Binary Quadratic Forms

scholarly journals A conjecture on the zeta functions of pairs of ternary quadratic forms

2021 ◽  
Vol 143 (2) ◽  
pp. 335-410
Author(s):  
Jin Nakagawa
Keyword(s):  
Quadratic Forms ◽  
Zeta Functions ◽  
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].

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

The representation of integers by positive ternary quadratic forms

Mathematika ◽  
1954 ◽  
Vol 1 (2) ◽  
pp. 104-110 ◽  
Author(s):  
G. L. Watson
Keyword(s):  
Quadratic Forms ◽  
Ternary Quadratic Forms ◽  
Representation Of Integers

scholarly journals Levels of positive definite ternary quadratic forms

1992 ◽  
Vol 58 (197) ◽  
pp. 399 ◽  
Author(s):  
J. Larry Lehman
Keyword(s):  
Quadratic Forms ◽  
Positive Definite ◽  
Ternary Quadratic Forms

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

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