Page 1

Displaying 1 – 3 of 3

Showing per page

Chebyshev bounds for Beurling numbers

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

Acta Arithmetica

The first author conjectured that Chebyshev-type prime bounds hold for Beurling generalized numbers provided that the counting function N(x) of the generalized integers satisfies the L¹ condition 1 | N ( x ) - A x | d x / x 2 < for some positive constant A. This conjecture was shown false by an example of Kahane. Here we establish the Chebyshev bounds using the L¹ hypothesis and a second integral condition.

Currently displaying 1 – 3 of 3

Page 1