Project: Three open questions in the theory of Beurling's generalized primes
2019-01-01 – 2019-12-31
- Abstract
The goal of this researrch project is to make significant progress in the understanding of three
remarkable open problems about Beurling generalized primes and integers. These questions are
related to:
• The quest for a general abstract prime number theorem.
• The Malliavin second problem on the error term in the approximation of the asymptotic density of
Beurling generalized integers.
• Does the prime number theorem implies in general the mean-value vanishing of the Möbius
function?
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- Journal Article
- open access
On the estimate M(x)=o(x) for Beurling generalized numbers
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A new generalized prime random approximation procedure and some of its applications
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- Journal Article
- A1
- open access
The optimal Malliavin-type remainder for Beurling generalized integers
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- Journal Article
- A1
- open access
On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems : a constructive approach
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- Journal Article
- A1
- open access
An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
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- Journal Article
- A1
- open access
Beurling integers with RH and large oscillation
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- Journal Article
- A1
- open access
Halász's theorem for Beurling generalized numbers