A Test for the Riemann Hypothesis
de Reyna, Juan Arias
Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, p. 159-170 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We prove that the Riemann Hypothesis holds if and only if $$I=\int_1^{+\infty}\bigl\{\Pi(x)-\Li(x)\bigr\}^2x^{-2}\,dx<+\infty$$ with $I=J$, where $J$ is some definite, computable real number ($1.266
Publié le : 2008-09-15
Classification:  Riemann hypothesis,  prime numbers,  Fourier Transform,  11M26 
@article{1229696537,
     author = {de Reyna, Juan Arias},
     title = {A Test for the Riemann Hypothesis},
     journal = {Funct. Approx. Comment. Math.},
     volume = {38},
     number = {1},
     year = {2008},
     pages = { 159-170},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229696537}
}

de Reyna, Juan Arias. A Test for the Riemann Hypothesis. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp.  159-170. http://gdmltest.u-ga.fr/item/1229696537/