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A note on the upper bound estimate of high-dimensional Cochrane sums

✍ Scribed by Huaning Liu

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
102 KB
Volume
125
Category
Article
ISSN
0022-314X

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✦ Synopsis

An upper bound estimate of high-dimensional Cochrane sums is given in this note using Weinstein's version of Deligne's estimate for the hyper-Kloosterman sum and a mean value theorem of Dirichlet L-functions.

πŸ“œ SIMILAR VOLUMES

On the order of the high-dimensional Coc
On the order of the high-dimensional Cochrane sum and its mean value
✍ Xu Zhefeng; Zhang Wenpeng πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 156 KB

The main purpose of this paper is to study the high-dimensional Cochrane sum and give a sharp estimate of its order by using properties of hyper-Kloosterman sum and the mean value theorems of Dirichlet L-functions.

An upper bound on the sum of squares of
An upper bound on the sum of squares of degrees in a graph
✍ D. de Caen πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 163 KB

Let G be a simple graph with n vertices, e edges and vertex degrees &, d2 ..... d~. It is proved that d2+ ... +d~<~e(2e/(n-1)+ n-2) when n~>2. This bound does not generalize to all sequences of positive integers. A comparison is made to another upper bound on d 2 +. β€’ -+ d 2, due to Sz6kely et al. (