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H 1 Prime numbers with preassigned digits

Auteurs : Swaenepoel, Cathy (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Bourgain (2015) estimated the number of prime numbers with a proportion $c$ > 0 of preassigned digits in base 2 ($c$ is an absolute constant not specified). We present a generalization of this result in any base $g$ ≥ 2 and we provide explicit admissible values for the proportion $c$ depending on $g$. Our proof, which adapts, develops and refines Bourgain’s strategy, is based on the circle method and combines techniques from harmonic analysis together with results on zeros of Dirichlet $L$-functions, notably a very sharp zero-free region due to Iwaniec.

    Keywords : prime numbers; digits; circle method; Fourier transform; Dirichlet L-functions

    Codes MSC :
    11A41 - Primes
    11A63 - Radix representation; digital problems
    11N05 - Distribution of primes

    Informations sur la rencontre

    Nom de la rencontre : Zeta Functions / Fonctions Zêta
    Organisateurs de la rencontre : Armana, Cécile ; Fiorilli, Daniel ; Jouve, Florent ; Louboutin, Stephane
    Dates : 02/12/2019 - 06/12/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2062.html

    Citation Data

    DOI : 10.24350/CIRM.V.19586403
    Cite this video as: Swaenepoel, Cathy (2019). Prime numbers with preassigned digits. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586403
    URI : http://dx.doi.org/10.24350/CIRM.V.19586403

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