Asymptotic formula for the mean value of a multiple trigonometric sum
โ Scribed by V. N. Chubarikov
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1978
- Tongue
- English
- Weight
- 574 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
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.
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 &1ร2<a<0. This is an improvement on Kiuchi's former result [2], which gives th
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.
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