Generalized Dedekind Eta-Functions and Generalized Dedekind Sums
نویسندگان
چکیده
منابع مشابه
Generating functions and generalized Dedekind sums
We study sums of the form ∑ ζ R(ζ), where R is a rational function and the sum is over all nth roots of unity ζ (often with ζ = 1 excluded). We call these generalized Dedekind sums, since the most well-known sums of this form are Dedekind sums. We discuss three methods for evaluating such sums: The method of factorization applies if we have an explicit formula for ∏ ζ(1− xR(ζ)). Multisection ca...
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In this paper we will study the number-theoretical properties of the expression v1 nkal rcka,, d(p; a I . . . . . an) = ( 1) n/2 ~ cot cot (1) k=l P P and of related finite trigonometric sums. In Eq. (I), p is a positive integer, a~ . . . . . a, are integers prime to p, and n is even (for n odd the sum is clearly equal to zero). There are two reasons for being interested in sums of this type. F...
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Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec (1997) on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums s(m,n) with m and n running over rather general sets. Our result extends earlier work of Myerson (1988) and Vardi (1987). Using different techniques, w...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.2307/1996714