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Formulas For The Fourier Coefficients Of Cusp Form For Some Quadratic Forms, Ahmet Tekcan
Formulas For The Fourier Coefficients Of Cusp Form For Some Quadratic Forms, Ahmet Tekcan
Turkish Journal of Mathematics
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.