On an additive function on the set of ideals of an arbitrary number field

Tianxin Cai

Acta Arithmetica (1995)

  • Volume: 70, Issue: 2, page 97-102
  • ISSN: 0065-1036

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Tianxin Cai. "On an additive function on the set of ideals of an arbitrary number field." Acta Arithmetica 70.2 (1995): 97-102. <http://eudml.org/doc/206747>.

@article{TianxinCai1995,
author = {Tianxin Cai},
journal = {Acta Arithmetica},
keywords = {asymptotic result; additive functions; Gaussian integers; prime ideals; Dedekind zeta-function},
language = {eng},
number = {2},
pages = {97-102},
title = {On an additive function on the set of ideals of an arbitrary number field},
url = {http://eudml.org/doc/206747},
volume = {70},
year = {1995},
}

TY - JOUR
AU - Tianxin Cai
TI - On an additive function on the set of ideals of an arbitrary number field
JO - Acta Arithmetica
PY - 1995
VL - 70
IS - 2
SP - 97
EP - 102
LA - eng
KW - asymptotic result; additive functions; Gaussian integers; prime ideals; Dedekind zeta-function
UR - http://eudml.org/doc/206747
ER -

References

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  1. [1] K. Alladi and P. Erdős, On an additive arithmetic function, Pacific J. Math. 71 (1977), 275-294. Zbl0359.10038
  2. [2] T. X. Cai, On the mean value estimate of a certain arithmetic function, Chinese Sci. Bull. 29 (1984), 1481-1484 (in Chinese). Zbl0733.11032
  3. [3] T. X. Cai, On an additive function on the Gaussian integers, Adv. in Math. (Beijing) 20 (2) (1991), 250. 
  4. [4] J. M. De Koninck and A. Ivić, Topics in Arithmetical Functions, Notas Mat., Amsterdam, 1980. Zbl0442.10032
  5. [5] J. M. De Koninck and A. Ivić, The distributions of the average prime divisors of an integer, Arch. Math. (Basel) 43 (1984), 37-43. Zbl0519.10027
  6. [6] P. Erdős and A. Ivić, Estimates for sums involving the largest prime factor of an integer and certain related additive functions, Studia Sci. Math. Hungar. 15 (1980), 183-199. 
  7. [7] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Leipzig, 1909. 
  8. [8] E. Landau, Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale, Leipzig, 1927. Zbl53.0141.09
  9. [9] A. Mercier, Comportement asymptotique de ∑ p ≤ x p a x / p k , Canad. Math. Bull. 30 (1987), 309-317. Zbl0631.10028
  10. [10] P. Zarzycki, On a certain additive function on the Gaussian integers, Acta Arith. 52 (1989), 75-90. Zbl0682.10032

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