Mathematical  Culture and Thought

Mathematical Culture and Thought

Behind the Scene Truth ‎of ‎Chebotarev's Density Theorem

Document Type : Survey

Author
Department of Mathematical Sciences‎, ‎Sharif University of Technology‎, ‎Iran
Abstract
By behind the scene truth, we mean interpretation of a mathematical result. This means that we setermine that mathematical result is manifestation of which higher truth. There, we will try to find that Chebotarev's density theorem, which both its formulation and its proof had a determining role in the history of algebraic number theory, is manifestation of which higher truth.
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[1]    Chebotarev’s density theorem, in Wikipedia, available at https://en.wikipedia.org/ wiki/Chebotarev%27s_density_theorem
[2]    Davenport, H., Multiplicative Number Theory, Springer, New York, 1980.
[3]    Frobenius, F., Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitutionen seiner Gruppe, Sitzber. Berl. Akad., (1896), 689-705.
[4]    Kosters, M., A short proof of a Chebotarev density theorem for function fields, Math. Commun., 22(2017), 227-233.
[5]    Lagarias, J. C., Odlyzko, A. M., Effective versions of the Chebotarev density theorem, in Algebraic Number Fields, L-Functions and Galois Properties, A. Fröhlich, ed., Academic Press, New York, 1977, 409-464.
[6]    Rastegar, A., Research project no.3: A formulation of Riemann hypothesis on hyperbolic 3-manifolds (2023), preprint.
[7]    Serre, J., Abelian l-Adic Representations and Elliptic Curves, AK Peters/CRC Press, New York, 1988.
[8]    Tschebotareff, N., Die Bestimmung der Dichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen Substitutionsklasse gehiiren, Math. Ann., 95(1926), 191-228.

  • Receive Date 21 June 2023
  • Accept Date 19 July 2023
  • Publish Date 22 July 2024