On sums over Gaussian integers
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- by D. G. Hazlewood PDF
- Trans. Amer. Math. Soc. 209 (1975), 295-310 Request permission
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
- J. H. Jordan, The divisibility of Gaussian integers by large Gaussian primes, Duke Math. J. 32 (1965), 503–509. MR 184921, DOI 10.1215/S0012-7094-65-03251-5 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
Additional Information
- © Copyright 1975 American Mathematical Society
- 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