A generalization of the Siegel-Walfisz theorem
HTML articles powered by AMS MathViewer
- by Larry Joel Goldstein PDF
- Trans. Amer. Math. Soc. 149 (1970), 417-429 Request permission
Abstract:
The uniform prime number theorem for primes in arithmetic progressions is generalized to the setting of Hecke L-series.References
- Emil Artin, The collected papers of Emil Artin, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1965. Edited by Serge Lang and John T. Tate. MR 0176888 K. Chandrasekharan, Lectures on the Riemann Zeta Function, Tata Institute of Fundamental Research, Bombay, 1953.
- E. Fogels, On the zeros of Hecke’s $L$-functions. I, II, Acta Arith. 7 (1961/62), 87–106, 131–147. MR 136585, DOI 10.4064/aa-7-2-87-106
- Larry Joel Goldstein, Analogues of Artin’s conjecture, Bull. Amer. Math. Soc. 74 (1968), 517–519. MR 223328, DOI 10.1090/S0002-9904-1968-11987-1 H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der Algebraischen Zahlkörper, 2nd ed., Physica-Verlag, Wurzburg, 1965. MR 33 #4045a.
- Serge Lang, Algebraic numbers, Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto-London, 1964. MR 0160763
- Takayoshi Mitsui, Generalized prime number theorem, Jpn. J. Math. 26 (1956), 1–42. MR 92814, DOI 10.4099/jjm1924.26.0_{1}
- Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0087685 C. L. Siegel, Über die Classenzahl Quadratischer Korper, Acta Arith. 1 (1937), 83-86.
- J. T. Tate, Fourier analysis in number fields, and Hecke’s zeta-functions, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 305–347. MR 0217026 N. Tchebotarev, Studien über Primzahldichtigkeiten. I, II, Kazan. Univ. Fiz. Mat. Obšč. Izv. Ser. 3 (1927), 14-20; 3 (1927), 1-17.
- E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, at the Clarendon Press, 1951. MR 0046485
- Arnold Walfisz, Zur additiven Zahlentheorie. II, Math. Z. 40 (1936), no. 1, 592–607 (German). MR 1545584, DOI 10.1007/BF01218882
- André Weil, Basic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 144, Springer-Verlag New York, Inc., New York, 1967. MR 0234930
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 149 (1970), 417-429
- MSC: Primary 10.65
- DOI: https://doi.org/10.1090/S0002-9947-1970-0274416-6
- MathSciNet review: 0274416