Oscillations of the error term in the prime number theorem
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-018-0884-x
Abstract: Let $${\sigma + i{\gamma}}$$σ+iγ be a zero of the Riemann zeta function to the right of the line $${\frac{1}{2} + it}$$12+it. We show that this zero causes large oscillations of the error term of the… read more here.
Keywords: term; error term; number theorem; oscillations error ... See more keywords
Advanced Mathematical Formulas to Calculate Prime Numbers
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DOI: 10.11648/j.mcs.20210606.12
Abstract: Prime numbers are the core of mathematics and specifically of number theory. The application of prime numbers in modern science, especially in computer science, is very wide. The importance of prime numbers has increased especially… read more here.
Keywords: prime number; advanced mathematical; calculate prime; mathematics ... See more keywords
On a Dynamical Approach to Some Prime Number Sequences
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DOI: 10.3390/e20020131
Abstract: We show how the cross-disciplinary transfer of techniques from dynamical systems theory to number theory can be a fruitful avenue for research. We illustrate this idea by exploring from a nonlinear and symbolic dynamics viewpoint… read more here.
Keywords: forbidden patterns; dynamical approach; number; number sequences ... See more keywords
Densities in certain three-way prime number races
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DOI: 10.4153/s0008414x20000747
Abstract: Abstract Let $a_1$ , $a_2$ , and $a_3$ be distinct reduced residues modulo q satisfying the congruences $a_1^2 \equiv a_2^2 \equiv a_3^2 \ (\mathrm{mod}\ q)$ . We conditionally derive an asymptotic formula, with an error… read more here.
Keywords: densities certain; certain three; prime number; way prime ... See more keywords