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On the Distribution of αp; Modulo One
Journal of the London Mathematical Society, 1983It was shown by Vinogradov (see Theorem 7, Chapter 4 of [18]) that, for e > 0, there are infinitely many solutions in primes p of the inequalitywhere {x} denotes the fractional part of x and y = 0.1. The value of γ was improved toby Kaufman [9]. On the Riemann Hypothesis he showed that one can take γ =¼ The method used actually shows that, for any real
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CHARACTERIZATIONS OF SHIFT‐INVARIANT DISTRIBUTIONS BASED ON SUMMATION MODULO ONE
Australian Journal of Statistics, 1994SummaryLet X1Y1,…, Yn be independent random variables. We characterize the distributions of X and Yj satisfying the equation {X+Y1++Yn}=dX, where {Z} denotes the fractional part of a random variable Z. In the case of full generality, either X is uniformly distributed on [0,1), or Yj has.a shifted lattice distribution and X is shift‐invariant.
Wilms, R.J.G., Thiemann, J.G.F.
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On the Distribution Modulo 1 of Exponential Sequences
Mathematical Notes, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the distribution of primitive roots modulo $p$
Publicationes Mathematicae Debrecen, 1998Summary: Let \(p\geq 3\) be a prime. For each primitive root \(x\) modulo \(p\) with \(1\leq x\leq p-1\), it is clear that there exists one and only one primitive root \(\bar x\) modulo \(p\) with \(1\leq\bar x \leq p-1\) such that \(x\bar x\equiv 1 \bmod p\).
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On the distribution of $��p^��+��$ modulo one
2016Error in the proof of the main Lemma where the large sieve is ...
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On the distribution of αp modulo one (II)
Science in China Series A: Mathematics, 2000Suppose that α is an irrational number and β is a real number. It is proved that there are infinitely many prime numbers p such that ‖ αp-β ‖＜ p -9/22 .
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Distribution Modulo One and Diophantine Approximation
2012This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade.
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On the Distribution Modulo 1 of q-Additive Functions
Acta Mathematica Hungarica, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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One Hundred Years Uniform Distribution Modulo One and Recent Applications to Riemann’s Zeta-Function
, 2014J. Steuding
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