scholarly journals On the representation of integers by quadratic forms

2007 ◽  
Vol 96 (2) ◽  
pp. 389-416 ◽  
Author(s):  
T. D. Browning ◽  
R. Dietmann
Keyword(s):  
Quadratic Forms ◽  
Representation Of Integers

scholarly journals REPRESENTATIONS OF INTEGERS BY TERNARY QUADRATIC FORMS

2010 ◽  
Vol 06 (01) ◽  
pp. 127-158 ◽  
Author(s):  
BEN KANE
Keyword(s):  
Quadratic Forms ◽  
Theta Series ◽  
Implied Constant ◽  
Cusp Forms ◽  
Local Conditions ◽  
Full List ◽  
Ternary Quadratic Forms ◽  
Representation Of Integers ◽  
Representations Of Integers

We investigate the representation of integers by quadratic forms whose theta series lie in Kohnen's plus space [Formula: see text], where p is a prime. Conditional upon certain GRH hypotheses, we show effectively that every sufficiently large discriminant with bounded divisibility by p is represented by the form, up to local conditions. We give an algorithm for explicitly calculating the bounds. For small p, we then use a computer to find the full list of all discriminants not represented by the form. Finally, conditional upon GRH for L-functions of weight 2 newforms, we give an algorithm for computing the implied constant of the Ramanujan–Petersson conjecture for weight 3/2 cusp forms of level 4N in Kohnen's plus space with N odd and squarefree.

Summation of Singular Series Corresponding to the Representation of Integers by Some Quadratic Forms in Fourteen Variables

2000 ◽  
Vol 7 (2) ◽  
pp. 355-372
Author(s):  
G. Lomadze
Keyword(s):  
Quadratic Forms ◽  
Singular Series ◽  
Representation Of Integers ◽  
Positive Integers

Abstract A sum of the singular series corresponding to the number of representations of positive integers by some diagonal quadratic forms with integral coefficients is obtained.

scholarly journals The Bases of and the Number of Representation of Integers

2013 ◽  
Vol 2013 ◽  
pp. 1-34
Author(s):  
Barış Kendirli
Keyword(s):  
Quadratic Forms ◽  
Fundamental Theorem ◽  
Class Group ◽  
Equivalence Classes ◽  
Explicit Formulas ◽  
Direct Sums ◽  
Representation Of Integers ◽  
Positive Integers

Following a fundamental theorem of Hecke, some bases of and are determined, and explicit formulas are obtained for the number of representations of positive integers by all possible direct sums (111 different combinations) of seven quadratic forms from the class group of equivalence classes of quadratic forms with discriminant −71 whose representatives are .

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