On the difference of consecutive numbers prime to n

C. Hooley

Displaying similar documents to “On the difference of consecutive numbers prime to n”

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On normal lattice configurations and simultaneously normal numbers

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Let $q, q_{1}, \dots, q_{s} \geq 2$ be integers, and let $α_{1}, α_{2}, \dots$ be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence ${(\{α_{m} q^{n}\}, \dots, \{α_{m + s - 1} q^{n}\})}_{m, n = 1}^{M N}$ coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences ${(x n)}_{n = 1}^{M N}$ in $s$ -dimensional unit cube $(s, M, N = 1, 2, \dots)$ . We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence ${(\{α_{1} q_{1}^{n}\}, \dots, \{α_{s} q_{s}^{n}\})}_{n = 1}^{N}$ (Korobov’s problem).

An integral involving the remainder term in the Piltz divisor problem

R. Sitaramachandrarao (1987)

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On partitions without small parts

J.-L. Nicolas, A. Sárközy (2000)

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Let $r (n, m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$ . By applying the saddle point method to the generating series, an asymptotic estimate is given for $r (n, m)$ , which holds for $n \to \infty$ , and $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .