In this paper, representations of positive integers by certain quadratic forms Q_p defined for odd prime p are examined. The number of representations of positive integer n by the quadratic form Q_p, is denoted by r(n;Q_p), obtained for p=3,5 and 7.\thinspace We prove that r(n;Q_p)=\rho (n;Q_p)+\vartheta (n;Q_p) for p=3,5 and 7, where \rho (n;Q_p) is the singular series and \vartheta (n;Q_p) is the Fourier coefficient of cusp form.
representation of numbers, quadratic forms, generalized theta series, Fourier coefficient of cusp forms
TEKCAN, AHMET (2005) "Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms," Turkish Journal of Mathematics: Vol. 29: No. 2, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol29/iss2/4