International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 908045, 12 pages
Generalized Newman Phenomena and Digit Conjectures on Primes
Departments of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Received 2 June 2008; Accepted 26 August 2008
Academic Editor: Wee Teck Gan
Copyright © 2008 Vladimir Shevelev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove that the ratio of the Newman sum over numbers
multiple of a fixed integer, which is not a multiple of 3, and the Newman
sum over numbers multiple of a fixed integer divisible by 3 is o(1)
when the upper limit of summing tends to infinity. We also discuss a
connection of our results with a digit conjecture on primes.