Dedekind sums and uniform distribution (mod 1)

1995 ◽  
Vol 11 (1) ◽  
pp. 62-67 ◽  
Author(s):  
Zheng Zhiyong
Keyword(s):  
Uniform Distribution ◽  
Dedekind Sums ◽  
Uniform Distribution Mod 1

scholarly journals A theorem in asymptotic number theory

1965 ◽  
Vol 5 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Jack P. Tull
Keyword(s):  
Number Theory ◽  
Uniform Distribution ◽  
Arithmetic Function ◽  
Asymptotic Number ◽  
Uniform Distribution Mod 1 ◽  
Multiplicative Arithmetic ◽  
Multiplicative Arithmetic Function

Let α(n) be a multiplicative arithmetic function. H. Delange [1] has proved that if |α(n)| ≦ 1 for all n and for a certain constant ρ, , where if ρ = 1 then then . He applied this result to several problems such as uniform distribution (mod 1) of certain types of sequences.

scholarly journals Walsh functions and uniform distribution mod $1$

1993 ◽  
Vol 45 (4) ◽  
pp. 555-563 ◽  
Author(s):  
Bruce G. Sloss ◽  
William F. Blyth
Keyword(s):  
Uniform Distribution ◽  
Walsh Functions ◽  
Uniform Distribution Mod 1

scholarly journals Fractional parts of Dedekind sums

2016 ◽  
Vol 12 (05) ◽  
pp. 1137-1147
Author(s):  
William D. Banks ◽  
Igor E. Shparlinski
Keyword(s):  
Number Theory ◽  
Uniform Distribution ◽  
Exponential Sums ◽  
Kloosterman Sums ◽  
Duke Math ◽  
Dedekind Sums ◽  
Bilinear Forms ◽  
Recent Improvement ◽  
Double Exponential ◽  
Invent Math

Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec [Bilinear forms with Kloosterman fractions, Invent. Math. 128 (1997) 23–43] on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums [Formula: see text] with [Formula: see text] and [Formula: see text] running over rather general sets. Our result extends earlier work of Myerson [Dedekind sums and uniform distribution, J. Number Theory 28 (1988) 233–239] and Vardi [A relation between Dedekind sums and Kloosterman sums, Duke Math. J. 55 (1987) 189–197]. Using different techniques, we also study the least denominator of the collection of Dedekind sums [Formula: see text] on average for [Formula: see text].

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