Chebyshev bounds for Beurling numbers
Harold G. Diamond ; Wen-Bin Zhang
Acta Arithmetica, Tome 161 (2013), p. 143-157 / Harvested from The Polish Digital Mathematics Library
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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/x2<∞ 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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:279243 
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     title = {Chebyshev bounds for Beurling numbers},
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Harold G. Diamond; Wen-Bin Zhang. Chebyshev bounds for Beurling numbers. Acta Arithmetica, Tome 161 (2013) pp. 143-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-2-4/