G'erald Tenenbaum

collaborators

3 papers

math.NT2026

On partial derivatives of some summatory functions

GÃ©rald Tenenbaum

Let $f$ be a real arithmetic function and let $g : [1, \infty [\to R$ be a smooth function. We describe two emblematic instances in which saddle-point estimates may be used to…

math.NT2026

On a family of arithmetic series related to the MÃ¶bius function

GÃ©rald Tenenbaum

Let $P^{-} (n)$ denote the smallest prime factor of a natural integer $n > 1$ . Furthermore let $I^¼$ and $I ¨ $ denote respectively the MÃ¶bius function and the number of distinct prime fa…

math.NT2025

On effective mean-values of arithmetic functions

Let $r, f$ be multiplicative functions with $r ⩾ 0$ , $f$ is complex valued, $∣ f ∣ ⩽ r$ , and $r$ satisfies some standard growth hypotheses. Let $x$ be large, and assum…