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Lenstra, H. W. jun.

On Artin’s conjecture and Euclid’s algorithm in global fields. (English) Zbl 0362.12012

Invent. Math. 42, 201-224 (1977).
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Cited in 14 Reviews
Cited in 63 Documents

MSC:

11R45 Density theorems
11N05 Distribution of primes
13F10 Principal ideal rings
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\textit{H. W. Lenstra jun.}, Invent. Math. 42, 201--224 (1977; Zbl 0362.12012)
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References:

[1] Aigner, A.: Quadratische und kubische Restkriterien für das Auftreten einer Fibonacci-Primitivwurzel. J. reine angew. Math.274/275, 139-140 (1975) · Zbl 0302.12002
[2] Artin, E.: Collected papers. Reading, Mass.: Addison-Wesley 1965 · Zbl 0146.00101
[3] Bilharz, H.: Primdivisoren mit vorgegebener Primitivwurzel. Math. Ann.114, 476-492 (1937) · Zbl 0016.34301
[4] Bombieri, E.: Counting points on curves over finite fields (d’après S.A. Stepanov), Sém. Bourbaki25 (1973), exp. 430, Lecture Notes in Mathematics383. Berlin-Heidelberg-New York: Springer 1974
[5] Cooke, G., Weinberger, P.J.: On the construction of division chains in algebraic number fields, with applications toSL 2. Commun. Algebra3, 481-524 (1975) · Zbl 0315.12001
[6] Goldstein, L.J.: Analogues of Artin’s conjecture. Trans. Amer. math. Soc.149, 431-442 (1970); Bull. Amer. math. Soc.74, 517-519 (1968) · Zbl 0201.05702
[7] Goldstein, L.J.: Density questions in algebraic number theory. Amer. math. Monthly78, 342-351 (1971) · Zbl 0211.38401
[8] Goldstein, L.J.: Some remarks on arithmetic density questions. Proc. Symp. Pure Math.24 (Analytic number theory), 103-110, Amer. math. Soc. 1973 · Zbl 0289.12013
[9] Hasse, H.: Über die Artinsche Vermutung und verwandte Dichtefragen. Ann. Acad. Sci. Fennicae, Ser. A,116 (1952) · Zbl 0047.04204
[10] Heilbronn, H.A.: On an inequality in the elementary theory of numbers. Proc. Cambridge Philos. Soc.33, 207-209 (1937) · JFM 63.0110.02
[11] Hooley, C.: On Artin’s conjecture. J. reine angew. Math.225, 209-220 (1967) · Zbl 0221.10048
[12] Hooley, C.: Applications of sieve methods to the theory of numbers. Cambridge: Cambridge University Press 1976 · Zbl 0327.10044
[13] Lang, S.: Algebraic number theory. Reading, Mass.: Addison-Wesley 1970 · Zbl 0211.38404
[14] Lehmer, D.H., Lehmer, Emma: Heuristics, anyone?, pp. 202-210. In: G. Szegö et al. (eds), Studies in mathematical analysis and related topics, Essays in honor of George Pólya, Stanford University Press, Stanford 1962
[15] Lenstra, Jr., H.W.: Perfect arithmetic codes of order one. In preparation
[16] Matthews, K.R.: A generalization of Artin’s conjecture for primitive roots. Acta arithmetica29, 113-146 (1976) · Zbl 0335.10007
[17] Möller, H.: Zur Verteilung der Restindizes ganzer Zahlen. Ber. Ges. Math. Datenverarbeitung, Bonn,57, 83-98 (1972) · Zbl 0241.10027
[18] Prachar, K.: Primzahlverteilung. Berlin-Heidelberg-New York: Springer 1957 · Zbl 0080.25901
[19] Queen, C.: Arithmetic euclidean rings. Acta arithmetica26, 105-113 (1974) · Zbl 0423.12013
[20] Queen, C.: Some arithmetic properties of subrings of function fields over finite fields. Arch. Math.26, 51-56 (1975) · Zbl 0303.12008
[21] Rieger, G.J.: Verallgemeinerung eines Satzes von Romanov und anderes. Math. Nachr.20, 107-122 (1959) · Zbl 0100.27503
[22] Ryser, H.J.: Combinatorial mathematics. Carus Math. Monographs14, Math. Ass. of America, 1963 · Zbl 0112.24806
[23] Samuel, P.: About euclidean rings. J. Algebra19, 282-301 (1971) · Zbl 0223.13019
[24] Shanks, D.: Fibonacci primitive roots. Fibonacci Qu.10, 163-168, 181 (1972); cf. ibidem Shanks, D.: Fibonacci primitive roots. Fibonacci Qu.11, 159-160 (1973)
[25] Shanks, D.: Review of: S. Yates, ?Prime period lengths?. Math. Comp.29, 1162-1163 (1975)
[26] Shanks, D.: Review of: R. Baillie, ?Data on Artin’s conjecture?. Math. Comp.29, 1164-1165 (1975)
[27] Vinogradov, A.I.: ArtinL-series and his conjectures. Proc. Steklov Inst. Math.112, 124-142 (1971) · Zbl 0293.12009
[28] Weil, A.: Sur les courbes algébriques et les variétés qui s’en déduisent. Paris: Hermann 1948 · Zbl 0036.16001
[29] Weinberger, P.J.: A counterexample to an analogue of Artin’s conjecture. Proc. Amer. math. Soc.35, 49-52 (1972) · Zbl 0259.12009
[30] Weinberger, P.J.: On euclidean rings of algebraic integers. Proc. Symp. Pure Math.24 (Analytic number theory), 321-332, Amer. math. Soc., 1973 · Zbl 0287.12012
[31] Western, A.E., Miller, J.C.P.: Tables of indices and primitive roots. Cambridge: University Press 1968 · Zbl 0175.32501
[32] Wrench, Jr., J.W.: Evaluation of Artin’s constant and the twin prime constant. Math. Comp.15, 396-398 (1961) · Zbl 0102.03304
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