Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Reviews and Descriptions of Tables and Books


Journal: Math. Comp. 29 (1975), 329-340
DOI: https://doi.org/10.1090/S0025-5718-75-99680-5
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] DANIEL SHANKS & JOHN W. WRENCH, JR., "Calculation of $ \pi $ to 100,000 decimals," Math. Comp., v. 16, 1962, pp. 76-99. MR 0136051 (24:B2090)
  • [2] UMT 46, Math. Comp., v. 23, 1969, pp. 679-680.
  • [3] DONALD E. KNUTH, "Euler's constant to 1271 places," Math. Comp., v. 16, 1962, pp. 275-281. MR 0148255 (26:5763)
  • [1] M. LAL & P. GILLARD, "On the equation $ \phi (n) = \phi (n + k)$," Math. Comp., v. 26, 1972, pp. 579-583. MR 0319391 (47:7935)
  • [2] KATHRYN MILLER, UMT 25, Math. Comp., v. 27, 1973, pp. 447-448.
  • [1] H. WADA, RMT 15, Math. Comp., v. 26, 1972, pp. 302-303.
  • [1] RICHARD P. BRENT, "Irregularities in the distribution of primes and twin primes," Math. Comp., v. 29, 1975, pp. 43-56 (this issue). MR 0369287 (51:5522)
  • [2] DANIEL SHANKS & JOHN W. WRENCH, JR., "Brun's constant," Math. Comp., v. 28, 1974, pp. 293-299; "Corrigendum", ibid, p. 1183. MR 0352022 (50:4510)
  • [1] J. v. NEUMANN & H. H. GOLDSTINE, "A numerical study of a conjecture of Kummer," MTAC, v. 7, 1953, pp. 133-134. MR 0055784 (14:1126d)
  • [2] EMMA LEHMER, "On the location of Gauss sums," MTAC, v. 10, 1956, pp. 194-202. MR 0086092 (19:123a)
  • [3] A. I. VINOGRADOV, "On the cubic Gaussian sum," Izv. Akad. Nauk SSSR Ser. Mat., v. 31, 1967, pp. 123-148. (Russian) MR 0207666 (34:7481)
  • [4] C.-E. FRÖBERG, "New results on the Kummer conjecture," BIT, v. 14, 1974, pp. 117-119. MR 0337728 (49:2497)
  • [5] DANIEL SHANKS, "The simplest cubic fields," Math. Comp., v. 28, 1974, pp. 1137-1152. MR 0352049 (50:4537)
  • [6] J. W. S. CASSELS, "On Kummer sums," Proc. London Math. Soc., v. 21, 1970, pp. 19-27. MR 0266895 (42:1797)
  • [1] MARIE NICOLE GRAS, "Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de Q." Crelle's J. (To appear.) MR 0389845 (52:10675)
  • [2] G. GRAS, "Sur les l-classes d'ideaux dans les extensions cycliques relatives de degre premier l," Thèse, Grenoble, 1972.
  • [3] MARIE-NICOLE MONTOUCHET, "Sur le nombre de classes du sous-corps cubique de $ {Q^{(p)}}(p \equiv 1(3))$," Thèse, Grenoble, 1971.
  • [4] DANIEL SHANKS, "The simplest cubic fields," Math. Comp., v. 28, 1974, pp. 1137-1152. MR 0352049 (50:4537)
  • [1] K. IWASAWA & C. SIMS, "Computation of invariants in the theory of cyclotomic fields," J. Math. Soc. Japan, v. 18, 1966, pp. 86-96. MR 34 #2560. MR 0202700 (34:2560)
  • [2] W. JOHNSON, "On the vanishing of the Iwasawa invariant $ {\mu _p}$ for $ p < 8000$," Math. Comp., v. 27, 1973, pp. 387-396. MR 0384748 (52:5621)
  • [3] W. JOHNSON, "Irregular prime divisors of the Bernoulli numbers," Math. Comp., v. 28, 1974, pp. 653-657. MR 0347727 (50:229)
  • [1] UMT 48, MTAC, v. 2, 1946, pp. 139-140.
  • [2] D. N. LEHMER, Factor Table for the First Ten Millions, Washington, D. C, 1909; also List of Prime Numbers from 1 to 10,006,721, Washington, D. C., 1914. (Both reprinted by Hafner Publishing Co., New York, 1956.)
  • [3] MTAC, v. 3, 1948, p. 222, N 93.
  • [1] R. B. LAKEIN & S. KURODA, UMT 38, Math. Comp., v., 24, 1970, pp. 491-493.
  • [2] R. B. LAKEIN, "Computation of the ideal class group of certain complex quartic fields. 11," Math. Comp., v. 29, 1975, pp. 137-144 (this issue). MR 0444605 (56:2955)
  • [1] R. B. LAKEIN, "Computation of the ideal class group of certain complex quartic fields," Math. Comp., v. 28, 1974, pp. 839-846. MR 0374090 (51:10290)
  • [2] D. SHANKS, UMT 10, Math. Comp., v. 23, 1969, pp. 213-214. MR 0262204 (41:6814)
  • [1] O. KOLBERG, "Congruences for the coefficients of the modular invariant $ j(\tau )$ modulo powers of 2," Univ. Bergen Arbok Naturvit. Rekke, v. 16, 1961.
  • [2] D. H. LEHMER, "Properties of the coefficients of the modular invariant $ J(\tau )$," Amer. J. Math., v. 64, 1942, pp. 488-502. MR 0006210 (3:272c)
  • [3] J. LEHNER, "Divisibility properties of the Fourier coefficients of the modular invariant $ J(\tau )$," Amer. J. Math., v. 71, 1949, pp. 136-148. MR 0027801 (10:357a)
  • [4] J. LEHNER, "Further congruence properties of the Fourier coefficients of the modular invariant $ J(\tau )$," Amer. J. Math., v. 71, 1949, pp. 337-386.
  • [5] M. NEWMAN, "Congruences for the coefficients of modular forms and for the coefficients of $ j(\tau )$," Proc. Amer. Math. Soc., v. 9, 1958, pp. 609-612. MR 0098729 (20:5184)
  • [6] A. VAN WIJNGAARDEN, "On the coefficients of the modular invariant $ J(\tau )$," Nederl. Akad. Wetensch. Proc. Ser. A, v. 16, 1953, pp. 389-400. MR 0058637 (15:403a)
  • [7] H. S. ZUCKERMAN, "The computation of the smaller coefficients of $ J(\tau )$," Bull. Amer. Math. Soc., v. 45, 1939, pp. 917-919. MR 0001769 (1:294d)
  • [1] DANIEL SHANKS, "A sieve method for factoring numbers of the form $ {n^2} + 1$," MTAC, v. 13, 1959, pp. 78-86. MR 0105784 (21:4520)
  • [2] DANIEL SHANKS, "On the conjecture of Hardy & Littlewood concerning the number of primes of the form $ {n^2} + a$," Math. Comp., v. 14, 1960, pp. 321-332. MR 0120203 (22:10960)
  • [3] DANIEL SHANKS, "Supplementary data and remarks concerning a Hardy-Littlewood conjecture," Math. Comp., v. 17, 1963, pp. 188-193. MR 0159797 (28:3013)
  • [1] P. POULET, "Table des nombres composés vérifiant le théorème de Fermat pour le module 2 jusqu'à 100.000.000," Sphinx, v. 8, 1938, pp. 42-52. For corrections see Math. Comp., v. 25, 1971, pp. 944-945, MTE 485; v. 26, 1972, p. 814, MTE 497. MR 0655816 (58:31707)
  • [2] P. ERDÖS, "On pseudoprimes and Carmichael numbers," Publ. Math. Debrecen, v. 4, 1956, pp. 201-206. MR 0079031 (18:18e)
  • [1] H. W. LLOYD TANNER, Proc London Math. Soc., v. 18, 1886-1887, pp. 214-234; v. 24, 1892-1893, pp. 223-272.


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-75-99680-5
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society