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Journal of the London Mathematical Society 2001 64(3):523-547; doi:10.1112/S0024610701002630
© 2001 by London Mathematical Society
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© The London Mathematical Society

Distribution of Binomial Coefficients and Digital Functions

Guy Barat and Peter J. Grabner

20 rue Fourcroy, 75017 Paris, France, barat{at}finanz.math.tu-graz.ac.at
Institut für Mathematik A, Technische Universität Graz Steyrergasse 30, 8010 Graz, Austria, peter.grabner{at}tugraz.at

Received 8 September 2000. Revision received 26 April 2001.

The distribution of binomial coefficients in residue classes modulo prime powers and with respect to the p-adic valuation is studied. For this purpose, general asymptotic results for arithmetic functions depending on blocks of digits with respect to q-ary expansions are established.


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