Beurling zeta functions, generalised primes, and fractal membranes

DOI10.1007/s10440-006-9063-0zbMath1133.11057arXivmath/0410270OpenAlexW1974595587MaRDI QIDQ851999

Michel L. Lapidus, Titus W. Hilberdink

Publication date: 27 November 2006

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410270

zbMATH Keywords

Beurling numbersfractal membranesgeneralized prime numbers

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Distribution of primes (11N05) Algebras and orders, and their zeta functions (11S45) Generalized primes and integers (11N80)

Related Items (17)

Asymptotics of the number of restricted partitions ⋮ Composition operators and generalized primes ⋮ Beurling integers with RH and large oscillation ⋮ Multiplicative functions with sum zero over Beurling generalized prime number systems ⋮ THE OPTIMAL MALLIAVIN-TYPE REMAINDER FOR BEURLING GENERALIZED INTEGERS ⋮ The average order of the Möbius function for Beurling primes ⋮ On logarithmic asymptotics for the number of restricted partitions in the exponential case ⋮ Completely multiplicative functions with sum zero over generalised prime systems ⋮ Note on a conjecture of Bateman and diamond concerning the abstract PNT with Malliavin-type remainder ⋮ Typical shape of elements in an arithmetical semigroup with exponentially growing prime counting function and deviations from the Bose-Einstein distribution ⋮ THE RIEMANN ZETA FUNCTION AS AN EQUIVARIANT DIRAC INDEX ⋮ Second moment of the Beurling zeta-function ⋮ Well-behaved Beurling primes and integers ⋮ Flows of Mellin transforms with periodic integrator ⋮ Asymptotic distribution of Beurling integers ⋮ On second moment of Selberg zeta-function for \(\sigma =1\) ⋮ An example in Beurling's theory of generalised primes

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