Journals / Turkish Journal of Mathematics / 2005 / Cilt: 29 - Sayı: 2
Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
- Pages
- 141–156
- DOI
- —
Abstract
In this paper, representations of positive integers by certain quadratic forms Qp defined for odd prime p are examined. The number of representations of positive integer n by the quadratic form Qp, is denoted by r(n;Qp), obtained for p=3,5 and 7.\thinspace We prove that r(n;Qp)=r (n;Qp)+\vartheta (n;Qp) for p=3,5 and 7, where r (n;Qp) is the singular series and \vartheta (n;Qp) is the Fourier coefficient of cusp form.
Özet
In this paper, representations of positive integers by certain quadratic forms Qp defined for odd prime p are examined. The number of representations of positive integer n by the quadratic form Qp, is denoted by r(n;Qp), obtained for p=3,5 and 7.\thinspace We prove that r(n;Qp)=r (n;Qp)+\vartheta (n;Qp) for p=3,5 and 7, where r (n;Qp) is the singular series and \vartheta (n;Qp) is the Fourier coefficient of cusp form.