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- W2761876109 abstract "We prove uniform versions of two classical results in analytic number theory. The first is an asymptotic for the number of points of a complete lattice $Lambda subseteq mathbb{R}^d$ inside the $d$-sphere of radius $R$. In contrast to previous works, we obtain error terms with implied constants depending only on $d$. Secondly, let $phi(s) = sum_n a(n) n^{-s}$ be a `well behaved' zeta function. A classical method of Landau yields asymptotics for the partial sums $sum_{n < X} a(n)$, with power saving error terms. Following an exposition due to Chandrasekharan and Narasimhan, we obtain a version where the implied constants in the error term will depend only on the `shape of the functional equation', implying uniform results for families of zeta functions with the same functional equation." @default.
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- W2761876109 date "2017-10-05" @default.
- W2761876109 modified "2023-10-12" @default.
- W2761876109 title "Uniform bounds for lattice point counting and partial sums of zeta functions" @default.
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