THE MERTENS FUNCTION AND THE PROOF OF THE RIEMANN'S HYPOTHESIS
Sghiar, Mohamed
HAL, hal-01667383 / Harvested from HAL
Text on HAL
I will prove that $M(n)=O(n^{\frac{1}{2}+\epsilon})$ where M is the function of Mertens, and I deduce a new proof of the Riemann's hypothesis.
Publié le : 2017-12-25
Classification:  Mertens,  Riemann zeta function,  Mertens function,  Riemann hypothesis,  Prime Number,  number theory,  law of prime numbers,  distribution of prime numbers,  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT],  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA],  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV],  [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA],  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM],  [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] 
@article{hal-01667383,
     author = {Sghiar, Mohamed},
     title = {THE MERTENS FUNCTION   AND THE PROOF OF THE RIEMANN'S HYPOTHESIS },
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01667383}
}

Sghiar, Mohamed. THE MERTENS FUNCTION   AND THE PROOF OF THE RIEMANN'S HYPOTHESIS . HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01667383/