International audienceLet $\vfi$ be Euler's function, $\ga$ be Euler's constant and $N_k$ be the product of the first $k$ primes. In this article, we consider the function $c(n) =(n/\vfi(n)-e^\ga\log\log n)\sqrt{\log n}$. Under Riemann's hypothesis, it is proved that $c(N_k)$ is bounded and explicit bounds are given while, if Riemann's hypothesis fails, $c(N_k)$ is not bounded above or below
We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi's rec...
We show that the Riemann Hypothesis is equivalent to the assertion (ym)∈ℓ2 where ymym is defined by ...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
International audienceLet $\vfi$ be Euler's function, $\ga$ be Euler's constant and $N_k$ be the pro...
AbstractFor every positive integer n, let Xn′ be the set of primitive Dirichlet characters modulo n....
International audienceLet h(n) denote the largest product of distinct primes whose sum is n. The mai...
AbstractLet φ be the Euler's function. A question of Rosser and Schoenfeld is answered, showing that...
In this short note, we prove that 4 π 2 x log x + O(x) n x ϕ x n 1 3 + 4 π 2 x log x + O(x), for x →...
AbstractIn 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta functio...
Here, we put forth two different proofs for the Riemann hypothesis. The first one is presented by us...
International audienceIn this note, we improve some results of Granville \& Soundararajan on the dis...
Denote by $\zeta$ the Riemann zeta function and let $\Theta$ be the supremum of the real parts of it...
We prove that the reciprocal sum $S_k(x)$ of the least common multiple of $k\geq 3$ positive integer...
This appendix to the beautiful paper of Ihara puts it in the context of infinite global fields of ou...
The Riemann hypothesis has been of great interest in the mathematics community since it was proposed...
We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi's rec...
We show that the Riemann Hypothesis is equivalent to the assertion (ym)∈ℓ2 where ymym is defined by ...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
International audienceLet $\vfi$ be Euler's function, $\ga$ be Euler's constant and $N_k$ be the pro...
AbstractFor every positive integer n, let Xn′ be the set of primitive Dirichlet characters modulo n....
International audienceLet h(n) denote the largest product of distinct primes whose sum is n. The mai...
AbstractLet φ be the Euler's function. A question of Rosser and Schoenfeld is answered, showing that...
In this short note, we prove that 4 π 2 x log x + O(x) n x ϕ x n 1 3 + 4 π 2 x log x + O(x), for x →...
AbstractIn 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta functio...
Here, we put forth two different proofs for the Riemann hypothesis. The first one is presented by us...
International audienceIn this note, we improve some results of Granville \& Soundararajan on the dis...
Denote by $\zeta$ the Riemann zeta function and let $\Theta$ be the supremum of the real parts of it...
We prove that the reciprocal sum $S_k(x)$ of the least common multiple of $k\geq 3$ positive integer...
This appendix to the beautiful paper of Ihara puts it in the context of infinite global fields of ou...
The Riemann hypothesis has been of great interest in the mathematics community since it was proposed...
We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi's rec...
We show that the Riemann Hypothesis is equivalent to the assertion (ym)∈ℓ2 where ymym is defined by ...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
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