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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 1, Pages 3–18 (Mi izv2289)  

This article is cited in 3 scientific papers (total in 3 papers)

Sur les formules explicites de théorie des nombres

A. Weil


Abstract: "Explicit formulas" in number theory express the sum of values of a function at the zeros of an $L$-series of an algebraic number field as a sum of local terms corresponding to all norms of this field. For the case of Hecke $L$-series, such formulas were found earlier by the author. In this paper they are derived for Artin–Hecke series corresponding to arbitrary finite-dimensional representations of the group $W_{k,K}$ – the standard extension of the idele class group of a global field $K$ using the Galois group of a finite extension $K/k$. In this connection it turns out that terms corresponding to archimedean and nonarchimedean norms can be written in unique form.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:1, 1–17

Bibliographic databases:

UDC: 511
MSC: Primary 12A70; Secondary 12A85
Received: 15.06.1971
Language:

Citation: A. Weil, “Sur les formules explicites de théorie des nombres”, Izv. Akad. Nauk SSSR Ser. Mat., 36:1 (1972), 3–18; Math. USSR-Izv., 6:1 (1972), 1–17

Citation in format AMSBIB
\Bibitem{Wei72}
\by A.~Weil
\paper Sur les formules explicites de th\'eorie des nombres
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 1
\pages 3--18
\mathnet{http://mi.mathnet.ru/izv2289}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=379440}
\zmath{https://zbmath.org/?q=an:0245.12010}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 1
\pages 1--17
\crossref{https://doi.org/10.1070/IM1972v006n01ABEH001866}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Venkov, “Spectral theory of automorphic functions, the Selberg zeta-function, and some problems of analytic number theory and mathematical physics”, Russian Math. Surveys, 34:3 (1979), 79–153  mathnet  crossref  mathscinet  zmath
    2. A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818  mathnet  crossref  mathscinet  isi  elib  elib
    3. T. Kleberger, B. Z. Moroz, “Weil groups and the distribution of prime ideals”, Proc. Steklov Inst. Math., 296 (2017), 132–141  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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