Counting integer points on quadrics with arithmetic weights

Kumaraswamy, V.

doi:10.1090/tran/8154

Counting integer points on quadrics with arithmetic weights
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by V. Vinay Kumaraswamy PDF

Trans. Amer. Math. Soc. 373 (2020), 6929-6959

Abstract:

Let $F \in \mathbf {Z}[\boldsymbol {x}]$ be a diagonal, non-singular quadratic form in four variables. Let $\lambda (n)$ be the normalised Fourier coefficients of a holomorphic Hecke form of full level. We give an upper bound for the problem of counting integer zeros of $F$ with $|\boldsymbol {x}| \leqslant X$, weighted by $\lambda (x_1)$.

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