Counting integer points on quadrics with arithmetic weights

V. Vinay Kumaraswamy

doi:10.1090/tran/8154

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arXiv · 1802.00780

Counting integer points on quadrics with arithmetic weights

V. Vinay Kumaraswamy

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Abstract

Let $F \in \mathbf{Z}[\boldsymbol{x}]$ be a diagonal, non-singular quadratic form in $4$ variables. Let $λ(n)$ 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 $|\boldsymbol{x}| \leq X$, weighted by $λ(x_1)$.

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V. Vinay Kumaraswamy. 2020-08-03. Counting integer points on quadrics with arithmetic weights. https://doi.org/10.1090/tran%2F8154

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