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Distribution Modulo One of αpγ + β for Special Classes of Primes
AxiomsLet α,β∈R with α≠0, and let γ∈(0,5/6). Define the set M1 to consist of primes p such that p+2 is almost prime, and let M2 be the set of primes of the form p=a2+b2+1.
Atanaska Georgieva, Tatiana L. Todorova
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Trigonometric approximation and uniform distribution modulo one [PDF]
Proceedings of the American Mathematical Society, 1988 We construct n n -dimensional versions of the Beurling and Selberg majorizing and minorizing functions and use them to prove results on trigonometric approximation and to prove an n n -dimensional version of the Erdös-Turán inequality. Finally, an application is given to counting solutions of polynomial congruences.
Todd Cochrane
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On the Distribution of αp Modulo One in Quadratic Number Fields [PDF]
Uniform distribution theory, 2021 Abstract We investigate the distribution of αp modulo one in quadratic number fields 𝕂 with class number one, where p is restricted to prime elements in the ring of integers of 𝕂. Here we improve the relevant exponent 1/4 obtained by the first- and third-named authors for imaginary quadratic number fields [On the distribution of αp ...
Baier, Stephan +2 more
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DISTRIBUTION MODULO ONE AND RATNER’S THEOREM
, 2007 Measure rigidity is a branch of ergodic theory that has recently contributed to the solution of some fundamental problems in number theory and mathematical physics. Examples are proofs of quantitative versions of the Oppenheim conjecture, related questions on the spacings between the values of quadratic forms, a proof of quantum unique ergodicity for ...
J. Marklof
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Well-distribution modulo one and the primes
Proceedings of the American Mathematical SocietyLet ( p n )
Champagne, J. +3 more
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Log-Like Functions and Uniform Distribution Modulo One
Uniform distribution theory, 2018 Abstract For a function f satisfying f ( x ) = o ((log x ) K
M. Rehberg
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On the distribution of $$\alpha p$$ modulo one over Piatetski-Shapiro primes
Indian Journal of Pure and Applied Mathematics, 2022 Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denotes the distance from $x$ to the nearest integer.
S. Dimitrov
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Uniform distribution modulo one: a geometrical viewpoint.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1981 MENDES FRANCE, M., DEKKING, F.M.
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The uniform distribution modulo one of certain subsequences of ordinates of zeros of the zeta function [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2023 On the assumption of the Riemann hypothesis and a spacing hypothesis for the nontrivial zeros $1/2+i\gamma$ of the Riemann zeta function, we show that the sequence \begin{equation*}\Gamma_{[a, b]} =\Bigg\{ \gamma : \gamma>0 \quad \mbox{and} \quad ...
Fatma Çiçek, S. Gonek
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On Uniform Distribution Modulo 1 and Functional Convergence
Uniform distribution theoryAbstract In this note, we study the convergence of functional sequences. A criterion for uniform distribution mod 1 is derived. Then we study the partitions, block sequences and the uniform distribution preserving mappings. In the last part, we prove that to each one to one sequence dense in [0, 1] a regular matrix summation method such ...
Milan Paštéka
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