Lower bounds for a certain class of error functions

• Autorzy: J. Herzog , P. R. Smith
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1991-1992
• Tom: 60
• Numer: 3
• Strony: 289-305

Daty

wydano

1992

otrzymano

1990-09-17

Twórcy

autor

J. Herzog

• J. W. Goethe-Universität, Fachbereich Mathematik, Robert-Mayer-Str. 6-10, D-6000 Frankfurt am Main, Federal Republic of Germany

autor

P. R. Smith

• J. W. Goethe-Universität, Fachbereich Mathematik, Robert-Mayer-Str. 6-10, D-6000 Frankfurt am Main, Federal Republic of Germany

Bibliografia

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• [2] R. Dedekind, Gesammelte mathematische Werke. Erster Band, R. Fricke, E. Noether and Ö. Ore (eds.), Vieweg, Braunschweig 1930.
• [3] P. Erdős, On the sum $∑_{k≤x}d(f(k))$, J. London Math. Soc. 27 (1952), 7-15.
• [4] P. Erdős and H. N. Shapiro, On the changes of sign of a certain error function, Canad. J. Math. 3 (1951), 375-385.
• [5] H. Halberstam and H.-E. Richert, On a result of R. R. Hall, J. Number Theory 11 (1979), 76-89.
• [6] J. Herzog and P. R. Smith, Asymptotic results on the distribution of integers possessing weak order (mod m), preprint, Frankfurt 1990.
• [7] G. J. Janusz, Algebraic Number Fields, Academic Press, New York 1973.
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• [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] E. Landau, Vorlesungen über Zahlentheorie, Chelsea, New York 1950.
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• [13] H. L. Montgomery, Fluctuations in the mean of Euler's phi function, Proc. Indian Acad. Sci. (Math. Sci.) 97 (1987), 239-245.
• [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.
• [15] J. H. Proschan, On the changes of sign of a certain class of error functions, Acta Arith. 17 (1971), 407-430.
• [16] H. Stevens, Generalizations of the Euler φ-function, Duke Math. J. 38 (1971), 181-186.
• [17] A. Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Deutsch. Verlag Wiss., Berlin 1963.