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Second moment of the Beurling zeta-function
Lithuanian Mathematical Journal, 2019Let \(1 < p_{1} \leq p_{2} \leq \dots \rightarrow \infty\) be a generalized prime number (g-prime) system and let \(1 = \nu_{1} < \nu_{2} \leq \dots\) be the increasing sequence of power-products of g-primes with \(a_{n}\) the corresponding multiplicity of \(\nu_{n}\). The g-prime system has a natural zeta function defined through \(\zeta(s) = \sum_{n}
Ramūnas Garunkštis +2 more
exaly +3 more sources
Studying the upper bound of Beurling zeta function in the strip (0,1)
Journal of Interdisciplinary MathematicsDuring the third decade of the last century, Arne Beurling stated the sense of the generalized prim systems. He said that any positive, increasingly real sequence started from any number greater than one precisely, and this sequence is called Beurling primes (or the generalized prim). They also mentioned that the fundamental Theorem of arithmetic gives
Safa Mohsen Abd Alzahra +1 more
exaly +2 more sources
On the distribution of Beurling integers [PDF]
Journal of Number Theory, 2005 Asymptotic behaviour of the counting function of Beurling integers is deduced from Chebyshev upper bound and Mertens formula for Beurling primes.
Fainleib, A.S.
exaly +2 more sources
On Second Moment of Selberg Zeta-Function for σ=1\sigma =1
Results in Mathematics, 2021Ramūnas Garunkštis +2 more
exaly
Bounding the log-derivative of the zeta-function
Mathematische Zeitschrift, 2021Felipe Gonçalves
exaly
Density estimates for the zeros of the Beurling ζ function in the critical strip
Mathematika, 2022Szilárd RÉVÉSZ
exaly
A Lower Bound in an Approximation Problem Involving the Zeros of the Riemann Zeta Function
Advances in Mathematics, 2002Jean-François Burnol
exaly
On PNT equivalences for Beurling numbers
Monatshefte Fur Mathematik, 2016Gregory Debruyne, Jasson Vindas
exaly
-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem
Journal of Number Theory, 2010exaly