Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On uniform elementary estimates of arithmetic sums

Author: Stefan A. Burr
Journal: Proc. Amer. Math. Soc. 39 (1973), 497-502
MSC: Primary 10H25
MathSciNet review: 0314784
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A simple, elementary method is given for deriving estimates of sums of arithmetic functions, the estimates being in a certain sense uniform over a class of functions appearing in the summation. The method is particularly well suited to estimates needed in applications of Selberg's sieve.

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

  • [1] P. T. Bateman, Proof of a conjecture of Grosswald, Duke Math. J. 25 (1958), 67-72. MR 19, 1040. MR 0091970 (19:1040a)
  • [2] J. P. Tull, Dirichlet multiplication in lattice point problems, Duke Math. J. 26 (1959), 73-80. MR 21 #659. MR 0101852 (21:659)
  • [3] -, Dirichlet multiplication in lattice point problems. II, Pacific J. Math. 9 (1959), 609-615. MR 21 #6362. MR 0107637 (21:6362)
  • [4] B. M. Wilson, Proofs of some formulae enunciated by Ramanujan, Proc. London Math. Soc. (2) 21 (1922), 235-255.
  • [5] E. C. Titschmarsh, The theory of the Riemann zeta-function, 2nd ed., Clarendon Press, Oxford, 1951. MR 13, 741. MR 0046485 (13:741c)
  • [6] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Oxford Univ. Press, London, 1960.
  • [7] S. A. Burr, An elementary solution of the Waring-Goldbach problem (to appear).
  • [8] H. N. Shapiro and J. Warga, On the representation of large integers as sums of primes. I, Comm. Pure Appl. Math. 3 (1950), 153-176. MR 12, 244. MR 0037323 (12:244c)
  • [9] A. O. Gel'fond and Ju. V. Linnik, Elementary methods in the analytic theory of numbers, Fizmatgiz, Moscow, 1962; English transl., Rand McNally, Chicago, Ill., 1965; Pergamon Press, New York, 1966. MR 32 #5575a, b; 34 #1252. MR 0201368 (34:1252)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10H25

Retrieve articles in all journals with MSC: 10H25

Additional Information

Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society