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On mean values of some arithmetic functions in number fields

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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.

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References

  1. K. Chandrasekharan and R. Narasimhan, The approximate functional equation for a class of zeta-functions, Math. Ann., 152 (1963), 30–64.

    Article  MathSciNet  MATH  Google Scholar 

  2. K. Chandrasekharan and R. Narasimhan, On the number of integral ideals in Galois extensions, Monatsh. Math., 95 (1983), 99–109.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Deza and L. Varukhina, On mean values of some arithmetic functions in number fields, Discrete Math., 308 (2008), 4892–4899.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. R. Heath-Brown, The growth rate of the Dedekind zeta-function on the critical line, Acta Arith., 49 (1988), 323–339.

    MathSciNet  MATH  Google Scholar 

  5. A. Ivić, The Riemann Zeta-Function, John Wiley & Sons (New York, 1985).

    MATH  Google Scholar 

  6. H. Iwaniec and E. Kowalski, Analytic Number Theory, Am. Math. Soc. Colloquium Publ., 53, Am. Math. Soc. (Providence, 2004).

    MATH  Google Scholar 

  7. E. Panteleeva, Dirichlet divisor problem in number fields, Math. Notes, (44), 3 (1988), 750–757.

    MathSciNet  Google Scholar 

  8. E. Panteleeva, On the mean values of certain arithmetic functions, Math. Notes, (55), 2 (1994), 178–184.

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan Shandong, 250100, China

    Guangshi Lü

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  1. Guangshi Lü
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Correspondence to Guangshi Lü.

Additional information

This work is supported in part by key project of the National Natural Science Foundation of China (Grant No. 11031004), Shandong Province Natural Science Foundation (Grant No. ZR2009AM007), and IIFSDU.

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Lü, G. On mean values of some arithmetic functions in number fields. Acta Math Hung 132, 348–357 (2011). https://doi.org/10.1007/s10474-010-0055-1

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  • DOI: https://doi.org/10.1007/s10474-010-0055-1

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