Accurate Computations of Euler Products over Primes in Arithmetic Progressions

Authors :: Ramaré Olivier
Institut de Mathématiques de Marseille (I2M)
Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
Centre National de la Recherche Scientifique (CNRS)
Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
Aix Marseille Université (AMU)
Aix-Marseille Université - Faculté des Sciences (AMU SCI)
Ramaré, Olivier
Source :: Functiones et Approximatio Commentarii Mathematici, Functiones et Approximatio Commentarii Mathematici, 2021, 65 (1), pp.33-45. ⟨10.7169/facm/1853⟩, Functiones et Approximatio Commentarii Mathematici, Poznań : Wydawnictwo Naukowe Uniwersytet im. Adama Mickiewicza, 2021, 65, ⟨10.7169/facm/1853⟩, Functiones et Approximatio Commentarii Mathematici, 2021, 65, ⟨10.7169/facm/1853⟩
Publication Year :: 2019
Publisher :: arXiv, 2019.
Abstract: 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 formula for the product of terms of the shape $F(1/p, 1/p^s)$ when $F$ is a two-variable polynomial with coefficients in $\mathbb{C}$ and satisfying some restrictive conditions.<br />Comment: 10 pages

ISSN :: 02086573
Database :: OpenAIRE
Journal :: Functiones et Approximatio Commentarii Mathematici, Functiones et Approximatio Commentarii Mathematici, 2021, 65 (1), pp.33-45. ⟨10.7169/facm/1853⟩, Functiones et Approximatio Commentarii Mathematici, Poznań : Wydawnictwo Naukowe Uniwersytet im. Adama Mickiewicza, 2021, 65, ⟨10.7169/facm/1853⟩, Functiones et Approximatio Commentarii Mathematici, 2021, 65, ⟨10.7169/facm/1853⟩
Accession number :: edsair.doi.dedup.....068857281c6a936b4ddfcab1f62b97ab
Full Text :: https://doi.org/10.48550/arxiv.1911.10991