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Asymptotic formula for the mean value of a multiple trigonometric sum

โœ Scribed by V. N. Chubarikov


Publisher
SP MAIK Nauka/Interperiodica
Year
1978
Tongue
English
Weight
574 KB
Volume
23
Category
Article
ISSN
0001-4346

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๐Ÿ“œ SIMILAR VOLUMES


An Asymptotic Formula for a Trigonometri
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We obtain a representation formula for the trigonometric sum f (m, n) and deduce from it the upper bound f(m, n) < (4/p 2 ) m log m+ (4/p 2 )(c -log(p/2)+2C G ) m+O(m/`log m), where C G is the supremum of the function G(t) :=; . k=1 log |2 sin pkt|/(4k 2 -1), over the set of irrationals. The coeffi

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โœ Wenpeng Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 124 KB

The main purpose of this paper is using the mean value theorem of the Dirichlet L-functions to study the distribution property of a sums analogous to the Dedekind sums, and give an interesting mean square value formula.

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โœ Naoki Yanagisawa ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 296 KB

An asymptotic formula for the mean square of the remainder term 2 a (x) is obtained for &10. It is an interesting problem to obtain an asymptotic formula for the mean square of 2 a (x). It is known by Meurman [4] that for &1ร‚2<a<0. This is an improvement on Kiuchi's former result [2], which gives th

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โœ Zhang Wenpeng; Yi Yuan ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 96 KB

The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the asymptotic property of the sums analogous to Dedekind sums and give a sharper first power mean value formula.

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In this paper we present a relation among the multiple zeta values which generalizes simultaneously the ``sum formula'' and the ``duality'' theorem. As an application, we give a formula for the special values at positive integral points of a certain zeta function of Arakawa and Kaneko in terms of mu