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math.NT2019
Accurate Computations of Euler Products over Primes in Arithmetic Progressions
Olivier Ramaré
This note provides truncated formulae with explicit error terms to compute Euler products over primes in arithmetic progressions of rational fractions. It further provides such a f…
math.NT2019
Fast multi-precision computation of some Euler products
Salma Ettahri, Olivier Ramaré, Léon Surel
For every modulus , we define a family of subsets of the multiplicative group for which the Euler product $\prod_{p\text{mo…
math.NT2017
Rationality of the zeta function of the subgroups of abelian -groups
Olivier Ramaré
Given a finite abelian -group , we prove an efficient recursive formula for where ranges over the subgroups of . 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 , almost every prime in has the expected of prime primitive roots in the interval $[x,x+x^{\frac{1…