O. Ramar'e

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20082025

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math.NT2017

Rationality of the zeta function of the subgroups of abelian $p$ -groups

Olivier Ramaré

Given a finite abelian $p$ -group $F$ , we prove an efficient recursive formula for $σ_{a} (F) = \sum_{H \leq F} ∣ H ∣^{a}$ where $H$ ranges over the subgroups of $F$ . We infer from…

math.NT2017

A Variant of the Truncated Perron's Formula and Primitive Roots

D. S. Ramana, O. Ramaré

We show under the Generalised Riemann Hypothesis that for every $δ > 0$ , almost every prime $q$ in $[Q, 2 Q]$ has the expected of prime primitive roots in the interval $[x,x+x^{\frac{1…

Rationality of the zeta function of the subgroups of abelian p-groups

A Variant of the Truncated Perron's Formula and Primitive Roots

Rationality of the zeta function of the subgroups of abelian $p$ -groups