Counting Primes in Residue Classes

Autor: Deléglise, Marc, Dusart, Pierre, Roblot, Xavier-François

Publikováno v: Mathematics of Computation, 2004 Jul 01. 73(247), 1565-1575.

Externí odkaz: https://www.jstor.org/stable/4099911

Dirichlet's Theorem on primes in arithmetic progressions, and Chebyshev's Bias

Autor: Slettan, Lars Tore Spånberg

Publikováno v: Slettan, Lars Tore Spånberg. Dirichlet's Theorem on primes in arithmetic progressions, and Chebyshev's Bias. Master thesis, University of Oslo, 2018

Externí odkaz: http://hdl.handle.net/10852/63384
https://www.duo.uio.no/bitstream/handle/10852/63384/1/Lars-Tore-Sp-nberg-Slettan--masteroppgave.pdf

Chebyshev's bias in dihedral and generalized quaternion Galois groups

Autor: Alexandre Bailleul

We study the inequities in the distribution of Frobenius elements in Galois extensions of the rational numbers with Galois groups that are either dihedral $D_{2n}$ or (generalized) quaternion $\mathbb H_{2n}$ of two-power order. In the spirit of rece

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::15ad75cbad5dccd69fc5919a4458e27e
https://hal.science/hal-02453465v2/document

Limiting Properties of the Distribution of Primes in an Arbitrarily Large Number of Residue Classes

Autor: Lucile Devin

Publikováno v: Canadian Mathematical Bulletin
Canadian Mathematical Bulletin, 2020, 63 (4), pp.837-849. ⟨10.4153/S0008439520000089⟩

We generalize current known distribution results on Shanks–Rényi prime number races to the case where arbitrarily many residue classes are involved. Our method handles both the classical case that goes back to Chebyshev and function field analogue

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::533a159dc98cbe6cd2b8f28335d13aa5
https://hal.archives-ouvertes.fr/hal-03345852

Chebyshev’s bias for analytic L -functions

Autor: Lucile Devin

Publikováno v: Mathematical Proceedings
Mathematical Proceedings, Cambridge University Press (CUP), 2020, 169 (1), pp.103-140. ⟨10.1017/S0305004119000100⟩

In this paper we discuss the generalizations of the concept of Chebyshev's bias from two perspectives. First we give a general framework for the study of prime number races and Chebyshev's bias attached to general $L$-functions satisfying natural ana

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43c0a8891d2fabb56e571df53b0b26f6
https://hal.archives-ouvertes.fr/hal-03345851