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Eliahou, S, Massé, B and Schneider, D (2013)

On the mantissa distribution of powers of natural and prime numbers

Acta Mathematica Hungarica, Volume 139, Issue 1 (2013), pp. 49-63, doi: 10.1007/s10474-012-0244-1.

ISSN/ISBN: 0236-5294 DOI: Not available at this time.



Abstract: Given a fixed integer exponent r≧1, the mantissa sequences of (n r ) n and of , where p n denotes the nth prime number, are known not to admit any distribution with respect to the natural density. In this paper however, we show that, when r goes to infinity, these mantissa sequences tend to be distributed following Benford’s law in an appropriate sense, and we provide convergence speed estimates. In contrast, with respect to the log-density and the loglog-density, it is known that the mantissa sequences of (n r ) n and of are distributed following Benford’s law. Here again, we provide previously unavailable convergence speed estimates for these phenomena. Our main tool is the Erdős–Turán inequality.


Bibtex:
@article {, AUTHOR = {Eliahou, Shalom and Massé, Bruno and Schneider, Dominique}, TITLE = {On the mantissa distribution of powers of natural and prime numbers}, JOURNAL = {Acta Mathematica Hungarica}, YEAR = {2012}, MONTH = {June}, PAGES = {1--15}, ISSN = {0236-5294}, DOI = {10.1007/s10474-012-0244-1}, URL = {http://www.akademiai.com/content/37M42117885580MK}, }


Reference Type: Journal Article

Subject Area(s): Number Theory