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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
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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?)

  • J. H. Jordan, The divisibility of Gaussian integers by large Gaussian primes, Duke Math. J. 32 (1965), 503–509. MR 184921
  • E. Landau, Vorlesungen über Zahlentheorie, Band 2, Leipzig, 1927, pp. 279-292.
  • 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
  • Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0087685

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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