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- W2996286720 abstract "We bound Kloosterman-like sums of the shape [ sum_{n=1}^N exp(2pi i (x floor{f(n)}+ y floor{f(n)}^{-1})/p), ] with integers parts of a real-valued, twice-differentiable function $f$ is satisfying a certain limit condition on $f''$, and $floor{f(n)}^{-1}$ is meaning inversion modulo~$p$. As an immediate application, we obtain results concerning the distribution of modular inverses inverses $floor{f(n)}^{-1} pmod{p}$. The results apply, in particular, to Piatetski-Shapiro sequences $ floor{t^c}$ with $cin(1,frac{4}{3})$. The proof is an adaptation of an argument used by Banks and the first named author in a series of papers from 2006 to 2009." @default.
- W2996286720 created "2019-12-26" @default.
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- W2996286720 date "2020-09-01" @default.
- W2996286720 modified "2023-09-25" @default.
- W2996286720 title "Kloosterman sums with twice-differentiable functions" @default.
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- W2996286720 doi "https://doi.org/10.7169/facm/1845" @default.
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