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On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
-
N. Kachakhidze
Published/Copyright:
February 23, 2010
Abstract
The systems of bases are constructed for the spaces of cusp forms Sk(Γ0(3), χ) (k≥6), Sk(Γ0(7), χ) (k≥3) and Sk(Γ0(11), χ) (k≥3). Formulas are obtained for the number of representation of a positive integer by the sum of k binary quadratic forms of the kind 
, of the kind 
and of the kind 
.
Key words and phrases.: Representation of numbers by quadratic forms; direct sum of quadratic forms; space of cusp forms; generalized multiple theta-series
Received: 1995-07-03
Published Online: 2010-02-23
Published in Print: 1998-February
© 1998 Plenum Publishing Corporation
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- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
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Keywords for this article
Representation of numbers by quadratic forms;
direct sum of quadratic forms;
space of cusp forms;
generalized multiple theta-series
Articles in the same Issue
- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
- Numerical Solutions to the Darboux Problem with the Functional Dependence
- On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
