International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 908045, 12 pages
doi:10.1155/2008/908045
Generalized Newman phenomena and digit conjectures on primes
Vladimir Shevelev
Departments of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Abstract
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.