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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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2015
There are 4 prime numbers less than 10; there are 25 primes less than 100; there are 168 primes less than 1000, and 1229 primes less than 10000. At what rate do the primes thin out? Today we use the notation π(x) to denote the number of primes less than or equal to x; so π(1000) = 168.
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There are 4 prime numbers less than 10; there are 25 primes less than 100; there are 168 primes less than 1000, and 1229 primes less than 10000. At what rate do the primes thin out? Today we use the notation π(x) to denote the number of primes less than or equal to x; so π(1000) = 168.
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Proof of the Riemann Hypothesis
It is well known that the Riemann zeta function can be analytically continued to the Dirichlet eta function, which converges in the critical strip and, therefore, provides non-trivial zeros in the region to share with the zeta function so as to help count the number of primes less than a given number.openaire +1 more source
Equivalent formulations of the Riemann hypothesis based on lines of constant phase
, 2018W. Schleich +6 more
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The Riemann Hypothesis in Characteristic p in Historical Perspective
, 2018P. Roquette
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