Let p 3 be a prime number, b 2 a primitive root mod p and z an integer, 1 z p&1. The digit expansion of zΓp with respect to the basis b has a period consisting of the first p&1 digits c 1 , ..., c p&1 . We express the variance \_ 2 of c 1 , ..., c p&1 in terms of the Dedekind sum s( p, b) and invest
Dedekind sums and uniform distribution
β Scribed by Gerald Myerson
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 281 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0022-314X
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## Abstract We construct some multiple Dedekind sums and relate them to the relative class number of an imaginary abelian number field. (Β© 2005 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
We study the number of lattice points in integer dilates of the rational polytope x k a k 41 ( ) where a 1 ; . . . ; a n are positive integers. This polytope is closely related to the linear Diophantine problem of Frobenius: given relatively prime positive integers a 1 ; . . . ; a n ; find the lar
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.