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Representations of positive integers by positive quadratic forms

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2011-01-01

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Southeast Asian Mathematical Soc-seams

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In this work we consider the representations of positive integers by quadratic forms F-1 = x(1)(2) + x(1)x(2) + 8x(2)(2) and G(1) = 2x(1)(2) + x(1)x(2) + 4x(2)(2) of discriminant 31 and we obtain some results concerning the modular forms (sci) (T; F, phi(tau s)). Moreover we construct a basis for the cusp form space S-4 (Gamma(0) (31), 1), and then we give some formulas for the number of representations of positive integer n by positive definite quadratic forms.

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Representations of positive integers by positive definite quadratic forms, Generalized theta series, Eisenstein series, Cusp form, Science & technology, Physical sciences, Mathematics

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