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 | 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.

**[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**

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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