AI Summary & Key Takeaways
AI InsightThe 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.
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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.