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  • 1 Department of Mathematics, Shandong University, Jinan Shandong 250100, China
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Abstract

Deza and Varukhina [3] established asymptotic formulae for some arithmetic functions in quadratic and cyclotomic fields. We generalize their results to any Galois extension of the rational field. During this process we rectify the main terms in their asymptotic formulae.

  • [1] Chandrasekharan, K., Narasimhan, R. 1963 The approximate functional equation for a class of zeta-functions Math. Ann. 152 3064 .

  • [2] Chandrasekharan, K., Narasimhan, R. 1983 On the number of integral ideals in Galois extensions Monatsh. Math. 95 99109 .

  • [3] Deza, E., Varukhina, L. 2008 On mean values of some arithmetic functions in number fields Discrete Math. 308 48924899 .

  • [4] Heath-Brown, D. R. 1988 The growth rate of the Dedekind zeta-function on the critical line Acta Arith. 49 323339.

  • [5] Ivić, A. 1985 The Riemann Zeta-Function John Wiley & Sons New York.

  • [6] Iwaniec, H., Kowalski, E. 2004 Analytic Number Theory Am. Math. Soc. Colloquium Publ. 53 Am. Math. Soc. Providence.

  • [7] Panteleeva, E. 1988 Dirichlet divisor problem in number fields Math. Notes 3 44 750757.

  • [8] Panteleeva, E. 1994 On the mean values of certain arithmetic functions Math. Notes 2 55 178184 .

  • [9] Swinnerton-Dyer, H. P. F. 2001 A Brief Guide to Algebraic Number Theory London Mathematical Society Student Texts 50 Cambridge University Press Cambridge.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)