Special values of the dilogarithm function

J. Loxton

Displaying similar documents to “Special values of the dilogarithm function”

On mean values of L-functions and short character sums with real characters

Matti Jutila (1975)

Acta Arithmetica

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Limitation to the asymptotic formula in Waring's problem

W. K. A. Loh (1996)

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On partitions without small parts

J.-L. Nicolas, A. Sárközy (2000)

Journal de théorie des nombres de Bordeaux

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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 $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .

Dirichlet series with functional equations and related arithmetical identities

K. Chandrasekharan, H. Joris (1973)

Acta Arithmetica

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On the difference of consecutive numbers prime to n

C. Hooley (1963)

Acta Arithmetica

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The renewal theorem for random walk in two-dimensional time

P. Ney, S. Wainger (1972)

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An integral involving the remainder term in the Piltz divisor problem

R. Sitaramachandrarao (1987)

Acta Arithmetica

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On normal lattice configurations and simultaneously normal numbers

Mordechay B. Levin (2001)

Journal de théorie des nombres de Bordeaux

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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).

A $q$ -logarithmic analogue of Euler’s sine integral

Nobushige Kurokawa, Masato Wakayama (2005)

Rendiconti del Seminario Matematico della Università di Padova

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The distribution of the sum-of-digits function

Michael Drmota, Johannes Gajdosik (1998)

Journal de théorie des nombres de Bordeaux

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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.