Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On sums over Gaussian integers


Author: D. G. Hazlewood
Journal: Trans. Amer. Math. Soc. 209 (1975), 295-310
MSC: Primary 10H99
DOI: https://doi.org/10.1090/S0002-9947-1975-0371842-6
MathSciNet review: 0371842
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The object of this paper is to give asymptotic estimates for some number theoretic sums over Gaussian integers. As a consequence of general estimates, asymptotic estimates with explicit error terms for the number of Gaussian integers with only ``large'' prime factors and for the number of Gaussian integers with only ``small'' prime factors are given.


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

  • [1] J. H. Jordan, The divisibility of Gaussian integers by large Gaussian primes, Duke Math. J. 32 (1965), 503–509. MR 0184921
  • [2] E. Landau, Vorlesungen über Zahlentheorie, Band 2, Leipzig, 1927, pp. 279-292.
  • [3] B. V. Levin and A. S. Faĭnleĭb, Application of certain integral equations to questions of the theory of numbers, Uspehi Mat. Nauk 22 (1967), no. 3 (135), 119–197 (Russian). MR 0229600
  • [4] Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0087685

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10H99

Retrieve articles in all journals with MSC: 10H99


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0371842-6
Keywords: Gaussian integers, norms of Gaussian integers, numbers with small prime factors, numbers with large prime factors, differential-difference equations
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society