Number Theory

    

Bernoulli Sums of Powers, Euleru2013maclaurin Formula and Proof that Riemann Hypothesis is True

Authors: Marco Rolando Burgos Chambi

On 1859, the german mathematician Georg Friedrich Bernhard Riemann made one of his most famouspublications "On the Number of Prime Numbers less than a Given Quantity" when he was developing hisexplicit formula to give an exact number of primes less than a given number x, in which he conjectured that"all non-trivial zeros of the zeta function have a real part equal to 1/2 ". Riemann was sure of his statement,but he could not prove it, remaining as one of the most important hypotheses unproven for 163 years.In this paper, we have to prove that the Riemann Hypothesis is true, based on the Bernoullipower sum, the Euleru2013Maclaurin formula and its relation with the Riemann Zeta function.

Comments: 13 Pages.

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Submission history

[v1] 2022-06-30 17:10:58
[v2] 2022-07-07 14:31:51
[v3] 2022-07-18 07:37:56

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