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The calculation of certain Dirichlet series


Authors: Daniel Shanks and John W. Wrench
Journal: Math. Comp. 17 (1963), 136-154
MSC: Primary 10.41; Secondary 10.03
DOI: https://doi.org/10.1090/S0025-5718-1963-0159796-4
Corrigendum: Math. Comp. 22 (1968), 699.
Corrigendum: Math. Comp. 22 (1968), 699.
Corrigendum: Math. Comp. 22 (1968), 246-247.
Corrigendum: Math. Comp. 17 (1963), 487-488.
MathSciNet review: 0159796
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References | Similar Articles | Additional Information

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  • [1] Daniel Shanks, ``On the conjecture of Hardy and Littlewood concerning the number of primes of the form $ {n^2} + a$,'' Math. Comp., v. 14, 1960, p. 321-332. MR 0120203 (22:10960)
  • [2] Daniel Shanks, ``Supplementary data and remarks concerning a Hardy-Littlewood conjecture,'' Math. Comp., v. 17, 1963, p. 188-193. MR 0159797 (28:3013)
  • [3] Daniel Shanks, ``On numbers of the form $ {n^4} + 1$,'' Math. Comp., v. 15, 1961, p. 186-189; Corrigendum, v. 16, 1962, p. 513. MR 0120184 (22:10941)
  • [4] Daniel Shanks, ``A note on Gaussian twin primes,'' Math. Comp., v. 14, 1960, p. 201-203. MR 0111724 (22:2586)
  • [5] Paul T. Bateman & Roger A. Horn, ``A heuristic asymptotic formula concerning the distribution of prime numbers,'' Math. Comp., v. 16,, 1962, p. 363-367. MR 0148632 (26:6139)
  • [6] Paul T. Bateman & Rosemarie M. Stemmler, ``Waring's problem in algebraic number fields and primes of the form $ ({{p}^{r}}-1)/({{p}^{d}}-1)$,'' Illinois J. Math., v. 6, 1962, p. 142-156. MR 0138616 (25:2059)
  • [7] J. W. L. Glaisher, ``The Bernoullian function,'' Quart. J. Pure Appl. Math., v. 29, 1898, p. 1-168.
  • [8] A. Fletcher, J. C. P. Miller, L. Rosenhead, & L. J. Comrie, An Index of Mathematical Tables, Second edition, Addison-Wesley, 1962. (See Vol. 1, Section 4.) MR 0142796 (26:365a)
  • [9] Edmund Landau, Elementary Number Theory, Chelsea, 1958, See Part 4, Chapters 6-8. MR 0092794 (19:1159d)
  • [10] G. B. Mathews, Theory of Numbers, Chelsea, 1961, (reprint). MR 0126402 (23:A3698)
  • [11] G. H. Hardy, Ramanujan, Chelsea, N. Y., 1959, p. 8.
  • [12] G. Pall, ``The distribution of integers represented by binary quadratic forms,'' Bull. Amer. Math. Soc., v. 49, 1943, p. 449. MR 0008084 (4:240g)
  • [13] Daniel Shanks & Larry P. Schmid, ``Variations on a theorem of Landau,'' (to appear)
  • [14] G. K. Stanley. ``Two assertions made by Ramanujan,'' J. London Math. Soc., v. 3, 1928, p. 232-237 and v. 4, 1929, p. 32.
  • [15] Daniel Shanks, ``The second-order term in the asymptotic expansion of $ B(x)$,'' (to appear)
  • [16] Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, v. I, Chelsea, N. Y., 1953, p. 494-498.
  • [17] R. Liénard, Tables fondamentales à 50 décimales des Sommes $ {S_n}$, $ {u_n}$, $ {\sum _n}$, Centre de Documentation universitaire, Paris, 1948.
  • [18] J. W. Wrench, Jr., $ {\pi ^{ \pm n}}$, MTAC, v. 1, 1943-1945, p. 452, UMT 38.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1963-0159796-4
Article copyright: © Copyright 1963 American Mathematical Society

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