Calculation of Dirichlet $L$-functions
HTML articles powered by AMS MathViewer
- by Robert Spira PDF
- Math. Comp. 23 (1969), 489-497 Request permission
Abstract:
A method for calculating Dirichlet $L$-series is presented along with the theory of residue class characters and their automatic generation. Tables are given of zeros of $L$series for moduliReferences
- D. Davies and C. B. Haselgrove, The evaluation of Dirichlet $L$-functions, Proc. Roy. Soc. London Ser. A 264 (1961), 122–132. MR 136052, DOI 10.1098/rspa.1961.0187
- D. Davies, An approximate functional equation for Dirichlet $L$-functions, Proc. Roy. Soc. London Ser. A 284 (1965), 224–236. MR 173352, DOI 10.1098/rspa.1965.0060
- J. Barkley Rosser, Real roots of Dirichlet $L$-series, Bull. Amer. Math. Soc. 55 (1949), 906–913. MR 32694, DOI 10.1090/S0002-9904-1949-09306-0
- J. Barkley Rosser, Real roots of real Dirichlet $L$-series, J. Research Nat. Bur. Standards 45 (1950), 505–514. MR 0041161, DOI 10.6028/jres.045.058
- William Judson LeVeque, Topics in number theory. Vols. 1 and 2, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1956. MR 0080682 J. V. Uspensky & M. A. Heaslet, Elementary Number Theory, McGraw-Hill, New York, 1939. MR 1, 38.
- Joseph J. Rotman, The theory of groups. An introduction, Allyn and Bacon, Inc., Boston, Mass., 1965. MR 0204499 S. Chowla, "Note on Dirichlet’s $L$-functions," Acta Arith., v. 1, 1935, pp. 113–114. N. G. Čudakov, Introduction to the Theory of Dirichlet’s $L$-functions, OGIZ, Moscow, 1947. (Russian) MR 11, 234. R. Spira, Check Values, Zeros and Fortran Programs for the Riemann Zeta Function and its First Three Derivatives, Technical Report No. 1, University of Tennessee Computing Center, 1965.
- Harold Davenport, Multiplicative number theory, Lectures in Advanced Mathematics, No. 1, Markham Publishing Co., Chicago, Ill., 1967. Lectures given at the University of Michigan, Winter Term, 1966. MR 0217022 L. Schoenfeld, "A generalization of the Euler-Maclaurin sum formula." (To appear.) E. Landau, Vorlesungen über Zahlentheorie, Vol. I, Chelsea, New York, 1950.
- Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen. 2 Bände, Chelsea Publishing Co., New York, 1953 (German). 2d ed; With an appendix by Paul T. Bateman. MR 0068565
- Daniel Shanks and John W. Wrench Jr., The calculation of certain Dirichlet series, Math. Comp. 17 (1963), 136–154. MR 159796, DOI 10.1090/S0025-5718-1963-0159796-4 Royal Society of London, Mathematical Tables Committee. Royal Society Depository for Unpublished Mathematical Tables. Table 80. (Copy in Pennsylvania State University Library.)
- Robert Spira, Residue class characters, Duke Math. J. 37 (1970), 633–637. MR 269584 RMT 72, Math. Comp., v. 17, 1963, pp. 463–464.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 489-497
- MSC: Primary 65.25; Secondary 10.00
- DOI: https://doi.org/10.1090/S0025-5718-1969-0247742-X
- MathSciNet review: 0247742