Gauss sums

Part 1 of ebook "A pythagorean introduction to number theory: Right triangles, sums of squares, and arithmetic" has presents the following content: foundational material; basic number theory; integral solutions to the pythagorean equation; what integers are areas of right triangles; what numbers are the edges of a right triangle; primes of the form 4k+1; gauss sums, quadratic reciprocity, and the jacobi symbol;...

143p dieptieuung 20-07-2023 4 2   Download

In this paper we explore a random process generated by the incomplete Gauss sums and establish an analogue of weak invariance principle for these sums. We focus our attention exclusively on a generalization of the limit distribution of the long incomplete Gauss sums given by the family of periodic functions analyzed by the author and Marklof.

11p danhdanh27 07-01-2019 17 2   Download

Elementary Number Theoryby W W L ChenPublisher: Macquarie University 2003Description:An introduction to the elementary techniques of number theory: division and factorization, arithmetic functions, congruences, quadratic residues, sums of integer squares, elementary prime number theory, Gauss sums and quadratic reciprocity.......

0p nunongnuna 05-04-2013 77 6   Download

Weyl group multiple Dirichlet series were associated with a root system Φ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker, Bump and Friedberg [4] provided n is sufficiently large; their coefficients involve n-th order Gauss sums. The case where n is small is harder, and is addressed in this paper when Φ = Ar . “Twisted” Dirichet series are considered, which contain the series of [4] as a special case.

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Scientists and mathematicians of the nineteenth century laid the foundation of telecommunication and wireless technology, which has affected all facets of modern society. In 1864, James C. Maxwell put forth fundamental relations of electromagnetic ®elds that not only summed up the research ®ndings of Laplace, Poisson, Faraday, Gauss, and others but also predicted the propagation of electrical signals through space. Heinrich Hertz subsequently veri®ed this in 1887 and Guglielmo Marconi successfully transmitted wireless signals across the Atlantic Ocean in 1900...

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