50
Views
20
CrossRef citations to date
0
Altmetric
Original Articles

A p-adic Study of the Partial Sums of the Harmonic Series

Pages 287-302 | Published online: 03 Apr 2012

REFERENCES

  • Batut , C. , Bernardi , D. , Cohen , H. and Olivier , M. User's Guide to Pari-GP. [Batut et al. 1993], This manual is part of the program distribution, available by anonymous ftp from the host pari@ceremab. u-bordeaux.fr
  • Bernoulli , J. 1713 . Ars Conjectandi 85 – 90 . Basel [Bernoulli 1713], Reprinted in Die Werke von Jakob Bernoulli, Birkhäuser, Basel, 1975, vol. 3, pp. 163–167. English translation in D. E. Smith, A Source Book in Mathematics, McGraw-Hill, New York, 1929; reprinted by Dover, New York, 1959
  • Buhler , J. , Crandall , R. , Ernvall , R. and Metsänkylä , T. 1993 . “Irregular primes and cyclotomic invariants to four million” . Math. Comp. , 61 : 151 – 153 . [Buhler et al. 1993]
  • Dickson , L. E. 1952 . History of the Theory of Numbers vol. 1 , New York : Chelsea. . [Dickson 1952]
  • Eswarathasan , A. and Levine , E. 1991 . “p-integral harmonic sums” . Discrete Math. , 91 : 249 – 257 . [Eswarathasan and Levine 1991]
  • Euler , L. 1738 . “Methodus generalis summandi progressiones” . Comment. Acad. Sci. Petrop. , 6 : 68 – 97 . [Euler 1738]
  • Gardiner , A. 1988 . “Four problems on prime power divisibility” . Amer. Math. Monthly , 95 : 926 – 931 . [Gardiner 1988]
  • Glaisher , J. W. L. 1900/01 . “A general congruence theorem relating to the Bernoullian function” . Proc. London Math. Soc. , 33 : 27 – 56 . [Glaisher 1901]
  • Guy , R. K. 1993 . “A quarter century of Monthly unsolved problems, 1969–1993” . American Math. Monthly , 100 : 945 – 949 . [Guy 1993]
  • Graham , R. L. , Knuth , D. E. and Patashnik , O. 1989 . Concrete Mathematics Reading , MA : Addison-Wesley. . [Graham et al. 1989]
  • Hardy , G. H. and Wright , E. M. 1960 . An Introduction to the Theory of Numbers, , 4th ed. Oxford : Oxford University Press. . [Hardy and Wright 1960]
  • Harris , T. E. 1963 . The Theory of Branching Processes Berlin : Springer. . [Harris 1963]
  • Lamperti , John . 1966 . Probability: A Survey of the Mathematical Theory New York : Benjamin. . [Lamperti 1966]
  • Mahler , K. 1981 . p-adic Numbers and Their Functions, , 2nd ed. Cambridge : Cambridge Univ. Press. . [Mahler 1981]
  • Ribenboim , P. 1979 . 13 Lectures on Fermat's Last Theorem New York : Springer. . [Ribenboim 1979]
  • Sándor , J. 1993 . Zentralblatt Math. , 764 : 11018 [Sándor 1993], review of [Eswarathasan and Levine 1991]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.