A sharpening of Li's criterion for the Riemann Hypothesis
Voros, André
HAL, hal-00022109 / Harvested from HAL
Text on HAL
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to \infty$ (with explicit $A>0$ and $B$). The approach also holds for more general zeta or $L$-functions.
Publié le : 2004-07-05
Classification:  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT],  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 
@article{hal-00022109,
     author = {Voros, Andr\'e},
     title = {A sharpening of Li's criterion for the Riemann Hypothesis},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00022109}
}

Voros, André. A sharpening of Li's criterion for the Riemann Hypothesis. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00022109/