Generalized Newman Phenomena and Digit Conjectures on Primes

الملخص EN

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.