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.
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