Chebyshev bounds for Beurling numbers

Harold G. Diamond, and Wen-Bin Zhang. "Chebyshev bounds for Beurling numbers." Acta Arithmetica 160.2 (2013): 143-157. <http://eudml.org/doc/279243>.

@article{HaroldG2013,
abstract = {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.},
author = {Harold G. Diamond, Wen-Bin Zhang},
journal = {Acta Arithmetica},
keywords = {Beurling generalized numbers; Chebyshev prime bounds; Fejér kernel estimates; Wiener theorems},
language = {eng},
number = {2},
pages = {143-157},
title = {Chebyshev bounds for Beurling numbers},
url = {http://eudml.org/doc/279243},
volume = {160},
year = {2013},
}

TY - JOUR
AU - Harold G. Diamond
AU - Wen-Bin Zhang
TI - Chebyshev bounds for Beurling numbers
JO - Acta Arithmetica
PY - 2013
VL - 160
IS - 2
SP - 143
EP - 157
AB - 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.
LA - eng
KW - Beurling generalized numbers; Chebyshev prime bounds; Fejér kernel estimates; Wiener theorems
UR - http://eudml.org/doc/279243
ER -