# Chebyshev bounds for Beurling numbers

Harold G. Diamond; Wen-Bin Zhang

Acta Arithmetica (2013)

- Volume: 160, Issue: 2, page 143-157
- ISSN: 0065-1036

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topHarold 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 -

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