The correspondence between theta series of ternary and quaternary quadratic forms

1994 ◽  
Vol 70 (6) ◽  
pp. 2097-2111
Author(s):  
V. G. Zhuravlev
Keyword(s):  
Quadratic Forms ◽  
Theta Series

On the space of generalized theta-series for certain quadratic forms in any number of variables

2019 ◽  
Vol 69 (1) ◽  
pp. 87-98
Author(s):  
Ketevan Shavgulidze
Keyword(s):  
Upper Bound ◽  
Quadratic Forms ◽  
Theta Series ◽  
Vector Spaces ◽  
Generalized Theta Series

Abstract An upper bound of the dimension of vector spaces of generalized theta-series corresponding to some nondiagonal quadratic forms in any number of variables is established. In a number of cases, an upper bound of the dimension of the space of theta-series with respect to the quadratic forms of five variables is improved and the basis of this space is constructed.

On the notion of Jacobi polynomials for codes

1997 ◽  
Vol 121 (1) ◽  
pp. 15-30 ◽  
Author(s):  
MICHIO OZEKI
Keyword(s):  
Quadratic Forms ◽  
Jacobi Polynomials ◽  
Theta Series ◽  
Positive Definite

In this paper, we introduce the notion of Jacobi polynomials for codes, and establish some fundamental features of it. This notion comes out of considerations on the various invariants of the codes (e.g. [22–24]); it has to do with Jacobi theta-series of positive definite quadratic forms (cf. [9], p. 82). Thus the name ‘Jacobi polynomials for codes’ traces this fact.

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.

scholarly journals Siegel theta series for indefinite quadratic forms

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
Christina Roehrig
Keyword(s):  
Differential Equation ◽  
Modular Forms ◽  
Quadratic Forms ◽  
Theta Series ◽  
Second Order ◽  
Transformation Behavior ◽  
Modular Transformation ◽  
Indefinite Quadratic

AbstractThe modular transformation behavior of theta series for indefinite quadratic forms is well understood in the case of elliptic modular forms due to Vignéras, who deduced that solving a differential equation of second order serves as a criterion for modularity. In this paper, we will give a generalization of this result to Siegel theta series.

Theta series of ternary and quaternary quadratic forms

1983 ◽  
Vol 73 (1) ◽  
pp. 151-156 ◽  
Author(s):  
J. S. Hsia ◽  
D. C. Hung
Keyword(s):  
Quadratic Forms ◽  
Theta Series

A proof of Hecke’s formula for binary quadratic forms

2019 ◽  
Vol 16 (02) ◽  
pp. 233-240
Author(s):  
Frank Patane
Keyword(s):  
Quadratic Form ◽  
Explicit Formula ◽  
Quadratic Forms ◽  
Theta Series ◽  
Binary Quadratic Form ◽  
Binary Quadratic Forms

In Mathematische Werke, Hecke defines the operator [Formula: see text] and describes their utility in conjunction with theta series of quadratic forms. In particular, he shows that the image of theta series associated to classes of binary quadratic forms in CL[Formula: see text] is again a theta series associated to a collection of forms in CL[Formula: see text]. We state and prove an explicit formula for the action of [Formula: see text] on a binary quadratic form of negative discriminant.

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