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Modular Properties of Theta-Functions and Representation of Numbers by Positive Quadratic Forms
Published/Copyright:
March 3, 2010
Abstract
By means of the theory of modular forms the formulas for a number of representations of positive integers by two positive quaternary quadratic forms of steps 36 and 60 and by all positive diagonal quadratic forms with seven variables of step 8 are obtain.
Key words and phrases.: Quadratic form; number of representations; modular form; generalized theta-function
Received: 1995-01-22
Published Online: 2010-03-03
Published in Print: 1997-August
© 1997 Plenum Publishing Corporation
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- A Multidimensional Singular Boundary Value Problem of the Cauchy–Nicoletti Type
- Non-Abelian Cohomology of Groups
- On the Absolute Convergence of Fourier Series
- On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation
- On the Global Solvability of the Cauchy Problem for Singular Functional Differential Equations
- Weighted Composition Operators on Bergman and Dirichlet Spaces
- Modular Properties of Theta-Functions and Representation of Numbers by Positive Quadratic Forms
Keywords for this article
Quadratic form;
number of representations;
modular form;
generalized theta-function
Articles in the same Issue
- A Multidimensional Singular Boundary Value Problem of the Cauchy–Nicoletti Type
- Non-Abelian Cohomology of Groups
- On the Absolute Convergence of Fourier Series
- On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation
- On the Global Solvability of the Cauchy Problem for Singular Functional Differential Equations
- Weighted Composition Operators on Bergman and Dirichlet Spaces
- Modular Properties of Theta-Functions and Representation of Numbers by Positive Quadratic Forms
