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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kloosterman sum ： ウィキペディア英語版 Kloosterman sum In mathematics, a Kloosterman sum is a particular kind of exponential sum. Let be natural numbers. Then :$K(a,b;m)=\backslash sum\_\; e^\; (ax+bx^$ *)}. Here ''x *'' is the inverse of modulo . They are named for the Dutch mathematician Hendrik Kloosterman, who introduced them in 1926〔Kloosterman, H. D. ''On the representation of numbers in the form ''ax''2 + ''by''2 + ''cz''2 + ''dt''2, Acta Mathematica 49 (1926), pp. 407–464〕 when he adapted the Hardy–Littlewood circle method to tackle a problem involving positive definite diagonal quadratic forms in four as opposed to five or more variables, which he had dealt with in his dissertation in 1924.〔Kloosterman, H. D. ''Over het splitsen van geheele positieve getallen in een some van kwadraten'', Thesis (1924) Universiteit Leiden〕 ==Context== The Kloosterman sums are a finite ring analogue of Bessel functions. They occur (for example) in the Fourier expansion of modular forms. There are applications to mean values involving the Riemann zeta function, primes in short intervals, primes in arithmetic progressions, the spectral theory of automorphic functions and related topics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kloosterman sum」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.