Lower bounds for a certain class of error functions

J. Herzog; P. R. Smith

Acta Arithmetica (1992)

  • Volume: 60, Issue: 3, page 289-305
  • ISSN: 0065-1036

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J. Herzog, and P. R. Smith. "Lower bounds for a certain class of error functions." Acta Arithmetica 60.3 (1992): 289-305. <http://eudml.org/doc/206439>.

@article{J1992,
author = {J. Herzog, P. R. Smith},
journal = {Acta Arithmetica},
keywords = {asymptotic results; generalized totients; Nagell totient; Schemmel totient; arithmetic function},
language = {eng},
number = {3},
pages = {289-305},
title = {Lower bounds for a certain class of error functions},
url = {http://eudml.org/doc/206439},
volume = {60},
year = {1992},
}

TY - JOUR
AU - J. Herzog
AU - P. R. Smith
TI - Lower bounds for a certain class of error functions
JO - Acta Arithmetica
PY - 1992
VL - 60
IS - 3
SP - 289
EP - 305
LA - eng
KW - asymptotic results; generalized totients; Nagell totient; Schemmel totient; arithmetic function
UR - http://eudml.org/doc/206439
ER -

References

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  1. [1] T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York 1976. 
  2. [2] R. Dedekind, Gesammelte mathematische Werke. Erster Band, R. Fricke, E. Noether and Ö. Ore (eds.), Vieweg, Braunschweig 1930. 
  3. [3] P. Erdős, On the sum k x d ( f ( k ) ) , J. London Math. Soc. 27 (1952), 7-15. 
  4. [4] P. Erdős and H. N. Shapiro, On the changes of sign of a certain error function, Canad. J. Math. 3 (1951), 375-385. Zbl0044.03903
  5. [5] H. Halberstam and H.-E. Richert, On a result of R. R. Hall, J. Number Theory 11 (1979), 76-89. 
  6. [6] J. Herzog and P. R. Smith, Asymptotic results on the distribution of integers possessing weak order (mod m), preprint, Frankfurt 1990. 
  7. [7] G. J. Janusz, Algebraic Number Fields, Academic Press, New York 1973. Zbl0307.12001
  8. [8] V. S. Joshi, Order free integers (mod m), in: Number Theory, Mysore 1981, Lecture Notes in Math. 938, Springer, New York 1982, 93-100. 
  9. [9] J. C. Lagarias and A. M. Odlyzko, Effective versions of the Chebotarev density theorem, in: Algebraic Number Fields: L-functions and Galois Properties, Proc. Sympos. Durham 1975, Academic Press, London 1977, 409-464. 
  10. [10] E. Landau, Über die zahlentheoretische Funktion μ(k), in: Collected Works, Vol. 2, L. Mirsky et al. (eds.), Thales Verlag, Essen 1986, 60-93. 
  11. [11] E. Landau, Vorlesungen über Zahlentheorie, Chelsea, New York 1950. 
  12. [12] F. Mertens, Über einige asymptotische Gesetze der Zahlentheorie, J. Reine Angew. Math. 77 (1874), 289-338. 
  13. [13] H. L. Montgomery, Fluctuations in the mean of Euler's phi function, Proc. Indian Acad. Sci. (Math. Sci.) 97 (1987), 239-245. Zbl0656.10042
  14. [14] S. S. Pillai and S. D. Chowla, On the error terms in some asymptotic formulae in the theory of numbers (I), J. London Math. Soc. 5 (1930), 95-101. Zbl56.0889.01
  15. [15] J. H. Proschan, On the changes of sign of a certain class of error functions, Acta Arith. 17 (1971), 407-430. Zbl0233.10027
  16. [16] H. Stevens, Generalizations of the Euler φ-function, Duke Math. J. 38 (1971), 181-186. Zbl0215.06702
  17. [17] A. Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Deutsch. Verlag Wiss., Berlin 1963. Zbl0146.06003

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