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On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
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D. Khosroshvili
Published/Copyright:
February 23, 2010
Abstract
A general formula is derived for the number of representations r(n; f) of a natural number n by diagonal quadratic forms f with five variables of level 16. For f belonging to one-class series, r(n; f) coincides with the sum of a singular series, while in the case of a many-class series an additional term is required, for which the generalized theta-function introduced by T. V. Vepkhvadze [Vepkhvadze, Acta Arithmetica 53: 433–990] is used.
Received: 1995-06-26
Revised: 1996-08-16
Published Online: 2010-02-23
Published in Print: 1998-February
© 1998 Plenum Publishing Corporation
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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
