Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
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.
Anahtar Kelimeler:
representation of numbers, quadratic forms, generalized theta series, Fourier coefficient of cusp forms
Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
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,
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
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