- Turkish Journal of Mathematics
- Vol: 29 Issue: 2
- Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
Authors : Ahmet Tekcan
Pages : 141-156
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : representation of numbers, quadratic forms, generalized theta series, Fourier coefficient of cusp forms