A bound for the least prime ideal in the Chebotarev density theorem. (English) Zbl 0401.12014


11R45 Density theorems
11R42 Zeta functions and \(L\)-functions of number fields


Zbl 0362.12011
Full Text: DOI EuDML


[1] Ankeny, N.C.: The least quadratic non-residue. Annals of Math.55, 65-72 (1952) · Zbl 0046.04006
[2] Bombieri, E.: Le grand crible dans la théorie analytique des nombres. Astérisque No. 18, Société Mathématique de France, Paris 1974
[3] Deuring, M.: Über den Tschebotareffschen Dichtigkeitssatz. Math. Annalen110, 414-415 (1934) · Zbl 0009.39403
[4] Fogels, E.: On the distribution of prime ideals. Acta Arithmetica7, 255-269 (1961/62) · Zbl 0114.02501
[5] Guinand, A.P.: A summation formula in the theory of prime numbers. Proc. London Math. Soc. (2)50, 107-119 (1948) · Zbl 0031.11003
[6] Heilbronn, H.: Zeta functions andL-functions. In: Algebraic Number Theory (J.W.S. Cassels and A. Fröhlich, eds.) pp. 204-230. New York, London: Academic Press, 1967
[7] 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.), pp. 409-464. New York, London: Academic Press 1977 · Zbl 0362.12011
[8] Landau, E.: Algebraische Zahlen, Göttingen 1927
[9] Stark, H.M.: Some effective cases of the Brauer-Siegel theorem. Inventiones math.23, 135-152 (1974) · Zbl 0278.12005
[10] Tschebotareff, N.: Die Bestimmung der Dichtigkeit einer Menge von Primzahlen welche zu einer gegebenen Substitutionenklasse gehören. Math. Annalen95, 191-228 (1926) · JFM 51.0149.04
[11] Turàn, P.: Eine neue Methode in der Analysis und deren Anwendungen. Budapest: Akademiai Kiadó 1953 · Zbl 0052.04601
[12] Weil, A.: Sur les ?formules explicites? de la théorie des nombres premiers. Comm. Sem. Math. Lund 252-265 (1952) · Zbl 0049.03205
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