• [1] Daniel Shanks, On the conjecture of Hardy & Littlewood concerning the number of primes of the form 𝑛²+𝑎, Math. Comp. 14 (1960), 320–332. MR 0120203 (22 #10960), http://dx.doi.org/10.1090/S0025-5718-1960-0120203-6
• [2] Daniel Shanks, Supplementary data and remarks concerning a Hardy-Littlewood conjecture, Math. Comp. 17 (1963), 188–193. MR 0159797 (28 #3013), http://dx.doi.org/10.1090/S0025-5718-1963-0159797-6
• [3] Daniel Shanks, On numbers of the form 𝑛⁴+1, Math. Comput. 15 (1961), 186–189. MR 0120184 (22 #10941), http://dx.doi.org/10.1090/S0025-5718-1961-0120184-6
• [4] Daniel Shanks, A note on Gaussian twin primes, Math. Comput. 14 (1960), 201–203. MR 0111724 (22 #2586), http://dx.doi.org/10.1090/S0025-5718-1960-0111724-0
• [5] Paul T. Bateman and Roger A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Math. Comp. 16 (1962), 363–367. MR 0148632 (26 #6139), http://dx.doi.org/10.1090/S0025-5718-1962-0148632-7
• [6] Paul T. Bateman and Rosemarie M. Stemmler, Waring’s problem for algebraic number fields and primes of the form (𝑝^{𝑟}-1)/(𝑝^{𝑑}-1), Illinois J. Math. 6 (1962), 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, and L. J. Comrie, An index of mathematical tables. Vol. I: Introduction. Part I: Index according to functions, Second edition, Published for Scientific Computing Service Ltd., London, by Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962. MR 0142796 (26 #365a)
• [9] Edmund Landau, Elementary number theory, Chelsea Publishing Co., New York, N.Y., 1958. Translated by J. E. Goodman. MR 0092794 (19,1159d)
• [10] G. B. Mathews, Theory of numbers, 2nd ed, Chelsea Publishing Co., New York, 1961. MR 0126402 (23 #A3698)
• [11] G. H. Hardy, Ramanujan, Chelsea, N. Y., 1959, p. 8.
• [12] Gordon Pall, The distribution of integers represented by binary quadratic forms, Bull. Amer. Math. Soc. 49 (1943), 447–449. MR 0008084 (4,240g), http://dx.doi.org/10.1090/S0002-9904-1943-07947-5
• [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 ,'' (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 , , , Centre de Documentation universitaire, Paris, 1948.
• [18] J. W. Wrench, Jr., , MTAC, v. 1, 1943-1945, p. 452, UMT 38.

Bibliography

[1]

Daniel Shanks, ``On the conjecture of Hardy and Littlewood concerning the number of primes of the form ,'' 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 ,'' 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 ,'' 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 ,'' (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 , , , Centre de Documentation universitaire, Paris, 1948.

[18]

J. W. Wrench, Jr., , MTAC, v. 1, 1943-1945, p. 452, UMT 38.