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Irregularities in the Distribution of Prime Numbers in a Beatty Sequence
Canadian mathematical bulletin, 2019We prove irregularities in the distribution of prime numbers in any Beatty sequence ${\mathcal{B}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$, where $\unicode[STIX]{x1D6FC}$ is a positive real irrational number of finite type.
Janyarak Tongsomporn, J. Steuding
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A note on the distribution of clusters and deserts of prime numbers
Indagationes mathematicaeIn this note we consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. By using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the claim that ...
Eugenio P. Balanzario
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The distribution of prime numbers
Russian Mathematical Surveys, 1990CONTENTS Introduction Chapter I. The Riemann zeta-function and its connection with primes § 1. Definition of and Euler's identity § 2. Continuation of to the half-plane § 3. Continuation of to the whole plane § 4. Functional properties of and § 5. Zeros of and primes § 6. Elementary theorems on the complex zeros of § 7. Theorems of de la Vallee Poussin
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The Distribution of Prime Numbers
1982In this chapter we give some basic results concerning the distribution of prime numbers. The reader will only require some knowledge of the calculus —this chapter is a first introduction to analytic number theory and we shall omit all the deeper investigations.
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The distribution of Bernoulli numbers modulo primes
Archiv der Mathematik, 1988For an odd prime \(p\), let \(I\) by any set of \(m\) consecutive integers contained in \(\{1,\ldots,p-1\}\). The author proves the following result about Bernoulli numbers \(B\): for any rational integer \(\alpha\), the number of \(n\) in \(I\) such that \(\sum^{p-2}_{k=1}B_ kn^{p-1-k}\equiv \alpha \bmod p\), does not exceed \(4.5m^{2/3}\).
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A Quantum Model of the Distribution of Prime Numbers and the Riemann Hypothesis
International Journal of Theoretical Physics, 2020V. Barbarani
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Distribution of monomial-prime numbers and Mertens sum evaluations
Indian journal of pure and applied mathematics, 2023Lin Feng, Huixi Li, Biao Wang
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Visual Representation of Prime Number Distribution
In ths research, we present an innovative vsual perspective to analyze the dstribution of prime numbers based on what the Hoy Quran descrbed n the story of the Companons of the Cave. The Holy Quran indicated in a simpfied way their explaining their spatia dstribution visually, and reveas the intimacy that each prme number in the set of numbers ...openaire +1 more source
The Distribution of Fibonacci Numbers Modulo Primes
The American Mathematical Monthly, 2021Mohammad Javaheri, Stephanie Cambrea
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