Page 1

Displaying 1 – 5 of 5

Showing per page

Optimality of Chebyshev bounds for Beurling generalized numbers

Harold G. Diamond, Wen-Bin Zhang (2013)

Acta Arithmetica

If the counting function N(x) of integers of a Beurling generalized number system satisfies both 1 x - 2 | N ( x ) - A x | d x < and x - 1 ( l o g x ) ( N ( x ) - A x ) = O ( 1 ) , then the counting function π(x) of the primes of this system is known to satisfy the Chebyshev bound π(x) ≪ x/logx. Let f(x) increase to infinity arbitrarily slowly. We give a construction showing that 1 | N ( x ) - A x | x - 2 d x < and x - 1 ( l o g x ) ( N ( x ) - A x ) = O ( f ( x ) ) do not imply the Chebyshev bound.

Currently displaying 1 – 5 of 5

Page 1