Results 11 to 20 of about 12,032 (167)
Fractional parts of Dedekind sums [PDF]
, 2015 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 $s(m,n)$
Banks, William D., Shparlinski, Igor E.
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On a family of sums of powers of the floor function and their links with generalized Dedekind sums [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper we are concerned with a family of sums involving the floor function. With r a nonnegative integer and n and m positive integers we consider the sums Sᵣ(n,m):=Σₖ₌₁ⁿ⁻¹[km/n]ʳ.
Steven Brown
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Tuples of polynomials over finite fields with pairwise coprimality conditions [PDF]
, 2018 Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v that satisfy given pairwise coprimality conditions.
Arias de Reyna Martínez, Juan +1 more
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On a sum analogous to Dedekind sum and its mean square value formula
International Journal of Mathematics and Mathematical Sciences, 2002 The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the asymptotic property of a sum analogous to Dedekind sum, and give an interesting mean square value formula.
Zhang Wenpeng
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On Restricted Averages of Dedekind Sums
International Mathematics Research Notices, 2023 Abstract We investigate the averages of Dedekind sums over rational numbers in the set $\mathscr {F}_{\alpha }(Q) = \{\,{v}/{w}\in \mathbb {Q}: 0<w\leq Q\,\}\cap \lbrack 0, \alpha )$ for fixed $\alpha \leq 1/2$. In previous work, we obtained asymptotics for $\alpha =1/2$, confirming a conjecture of Ito in a quantitative form.
Minelli, Paolo +2 more
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Generalized equivalence of matrices over Prüfer domains
International Journal of Mathematics and Mathematical Sciences, 1991 Two m×n matrices A,B over a commutative ring R are equivalent in case there are invertible matrices P, Q over R with B=PAQ. While any m×n matrix over a principle ideal domain can be diagonalized, the same is not true for Dedekind domains.
Frank DeMeyer, Hainya Kakakhail
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Almost triangular matrices over Dedekind domains
International Journal of Mathematics and Mathematical Sciences, 1999 Every matrix over a Dedekind domain is equivalent to a direct sum of matrices A=(ai,j), where ai,j=0 whenever j>i+1.
Frank Demeyer, Haniya Kakakhail
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Transformation of Some Lambert Series and Cotangent Sums
Mathematics, 2019 By considering a contour integral of a cotangent sum, we give a simple derivation of a transformation formula of the series A ( τ , s ) = ∑ n = 1 ∞ σ s − 1 ( n ) e 2 π i n τ for complex s ...
Namhoon Kim
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The reciprocity theorem for Dedekind sums [PDF]
Pacific Journal of Mathematics, 1953 Let \(((x)) = x - [x] - \tfrac12\) where \([x]\) denotes the integral part of \(x\). Define the Dedekind sum \(S(h, k)\) by \[ S(h, k) = \sum_{r\pmod k} \left(\left(\frac{r}{k}\right)\right) \left(\left(\frac{rh}{k}\right)\right). \] Dedekind and later various authors proved the reciprocity formula \[ 12hk (S(h, k) + S(k, h)) = h^2 + 3kh + k^2 + 1 \tag{
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Upper bound estimate of incomplete Cochrane sum
Open Mathematics, 2017 By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.
Ma Yuankui, Peng Wen, Zhang Tianping
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