Chebyshev bounds for Beurling numbers

• Autorzy: Harold G. Diamond , Wen-Bin Zhang
• Języki publikacji: EN

Abstrakty

EN

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
$∫_1^∞ |N(x) - Ax| dx/x^2 < ∞$
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.

Kategorie tematyczne

• 11N80: Generalized primes and integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 2
• Strony: 143-157

Daty

wydano

2013

Twórcy

autor

Harold G. Diamond

• Department of Mathematics, University of Illinois, Urbana, IL 61801, U.S.A.

autor

Wen-Bin Zhang

• 920 West Lawrence Ave. #1112, Chicago, IL 60640, U.S.A.

Identyfikatory

DOI

10.4064/aa160-2-4