Keywords
- Asymptotic Formula
- Arithmetic Progression
- Average Order
- Arithmetical Function
- Divisor Problem
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References
Abramowitz, M., and Stegun, I.: Handbook of mathematical functions. New York 1964.
Berndt, B.: On the average order of a class of arithmetical functions, I. J. Number Theory 3, 184–203 (1971).
Berndt, B.: On the average order of a class of arithmetical functions, II. J. Number Theory 3, 288–305 (1971).
Chandrasekharan, K., and Narasimhan, R.: Functional equations with multiple gamma factors and the average order of a class of arithmetical functions. Ann. of Math. 76, 93–136 (1962).
Chandrasekharan, K., and Narasimhan, R.: Approximate functional equations for a class of zeta-functions. Math. Ann. 152, 30–64 (1963).
Epstein, P.: Zur Theorie allgemeiner Zetafunctionen. Math. Ann. 56, 615–644 (1902).
Hafner, J. L.: On the average order of a class of arithmetical functions. J. Number Theory 15, 36–76 (1982).
Hafner, J. L.: The distribution and average order of the coefficients of Dedekind ζ-functions. J. Number Theory 17, 183–190 (1983).
Hlawka, E., and Schoißengeier, J.: Zahlentheoric. 1. Aufl. Wien 1979.
Jenkner, W.: Ein Teilerproblem in Restklassen von ℤ[i]. Preprint.
Landau, E.: Zur analytischen Zahlenthcoric der definiten quadratischen Formen. (Über die Gitterpunkte in einem mehrdimensionalen Ellipsoid.) Sitz.-Ber. Berlin 31, 458–476 (1915).
Menzer, H., and Nowak, W. G.: On an asymmetric divisor problem with congruence conditions. Manuscr. math. 64, 107–119 (1989).
Müller, W., and Nowak, W.G.: Lattice points in planar domains: Applications of Huxley's ‘Discrete Hardy-Littlewood method'. In this volume.
Nowak, W. G.: On a result of Smith and Subbarao concerning a divisor problem. Canad. Math. Bull. 27, 501–504 (1984).
Nowak, W. G.: On a divisor problem in arithmetic progressions. J. Number Theory 31, 174–182 (1989).
Smith, A., and Subbarao, M. V.: The average number of divisors in an arithmetic progression. Canad. Math. Bull. 24, 37–41 (1981).
Steinig, J.: On an integral connected with the average order of a class of arithmetical functions. J. Number Theory 4, 463–468 (1972).
Szegö, P. and Walfisz, A.: Über das Piltzsche Teilerproblem in algebraischen Zahlkörpern (Erste Abhandlung). Math. Z. 26, 138–156 (1927).
Szegö, P. and Walfisz, A.: Über das Piltzsche Teilerproblem in algebraischen Zahlkörpern (Zweite Abhandlung). Math. Z. 26, 138–156 (1927).
Van der Waerden, B. L.: Moderne Algebra. Erster Teil. Berlin 1930.
Varbanec, P. D., and Zarzycki, P.: Divisors of the Gaussian integers in an arithmetic progression. J. Number Theory 33, 152–169 (1989).
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© 1990 Springer-Verlag
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Nowak, W.G. (1990). Divisors in arithmetic progressions in imaginary quadratic number fields. In: Hlawka, E., Tichy, R.F. (eds) Number-Theoretic Analysis. Lecture Notes in Mathematics, vol 1452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096989
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DOI: https://doi.org/10.1007/BFb0096989
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