- Turkish Journal of Mathematics
- Volume: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 : 8 | Download : 7
Publication Date : 0000-00-00
Article Type : Research Paper
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 rinsert ignore into journalissuearticles values(n;Qp);, obtained for p=3,5 and 7.\thinspace We prove that rinsert ignore into journalissuearticles values(n;Qp);=r insert ignore into journalissuearticles values(n;Qp);+\vartheta insert ignore into journalissuearticles values(n;Qp); for p=3,5 and 7, where r insert ignore into journalissuearticles values(n;Qp); is the singular series and \vartheta insert ignore into journalissuearticles values(n;Qp); is the Fourier coefficient of cusp form.Keywords : representation of numbers, quadratic forms, generalized theta series, Fourier coefficient of cusp forms