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Displaying 101 – 120 of 174

On the behaviour close to the unit circle of the power series with Möbius function coefficients

Oleg Petrushov (2014)

Acta Arithmetica

Let $(z) = \sum_{n = 1}^{\infty} μ (n) z^{n}$ . We prove that for each root of unity $e (β) = e^{2 π i β}$ there is an a > 0 such that $(e (β) r) = Ω ({(1 - r)}^{- a})$ as r → 1-. For roots of unity e(l/q) with q ≤ 100 we prove that these omega-estimates are true with a = 1/2. From omega-estimates for (z) we obtain omega-estimates for some finite sums.

On the Bombieri-Korobov estimate for Weyl sums

Scott T. Parsell (2009)

Acta Arithmetica

On the Brun-Titchmarsh theorem.

Christopher Hooley (1972)

Journal für die reine und angewandte Mathematik

On the class number of binary quadratic forms: An omega estimate for the error term.

Kühleitner, Manfred (2002)

Mathematica Pannonica

On the constant factor in Vinogradov's Mean Value Theorem

Géza Kós (2001)

Acta Arithmetica

On the cycle structure of linear recurring sequences.

H. Niederreiter (1976)

Mathematica Scandinavica

On the degree of the $L$ -function associated with an exponential sum

Alan Adolphson, Steven Sperber (1988)

Compositio Mathematica

On the determination of Gauss sums

John H. Loxton (1976/1977)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

On the determination of generalized Gauss sums

J. W. S. Cassels (1969)

Archivum Mathematicum

On the diaphony of some finite hybrid point sets

Peter Hellekalek, Peter Kritzer (2012)

Acta Arithmetica

On the difference between a D. H. Lehmer number and its inverse modulo q

Wenpeng Zhang (1994)

Acta Arithmetica

On the difference between consecutive squarefree integers

S. Graham, G. Kolesnik (1988)

Acta Arithmetica

On the difference of the consecutive primitive roots

Yonghui Wang, Claus Bauer (2004)

Acta Arithmetica

On the Dirichlet characters of polynomials in several variables

Wenpeng Zhang, Zhefeng Xu (2006)

Acta Arithmetica

On the discrepancy of sequences associated with the sum-of-digits function

Gerhard Larcher, N. Kopecek, R. F. Tichy, G. Turnwald (1987)

Annales de l'institut Fourier

If $w = (q_{k})_{k \in N}$ denotes the sequence of best approximation denominators to a real $α$ , and $s_{α} (n)$ denotes the sum of digits of $n$ in the digit representation of $n$ to base $w$ , then for all $x$ irrational, the sequence $(s_{α} (n) \cdot x)_{n \in N}$ is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if $α$ has bounded continued fraction coefficients.

On the discrepancy of some hybrid sequences

Harald Niederreiter (2009)

Acta Arithmetica

On the distribution modulo 1 of the sequence $α n^{3} + β n^{2} + γ n$

R. Baker (1981)

Acta Arithmetica

On the distribution of consecutive square-free primitive roots modulo $p$

Huaning Liu, Hui Dong (2015)

Czechoslovak Mathematical Journal

A positive integer $n$ is called a square-free number if it is not divisible by a perfect square except $1$ . Let $p$ be an odd prime. For $n$ with $(n, p) = 1$ , the smallest positive integer $f$ such that $n^{f} \equiv 1 (mod p)$ is called the exponent of $n$ modulo $p$ . If the exponent of $n$ modulo $p$ is $p - 1$ , then $n$ is called a primitive root mod $p$ . Let $A (n)$ be the characteristic function of the square-free primitive roots modulo $p$ . In this paper we study the distribution $\sum_{n \leq x} A (n) A (n + 1),$ and give an asymptotic formula by using properties of character sums.

On the distribution of distances between the points of affine curves over finite fields.

Petrenko, B.V. (2005)

Integers

On the distribution of exponential sums.

Konyagin, Sergei V., Lev, Vsevolod F. (2000)

Integers

Currently displaying 101 – 120 of 174

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