11 citations · 11 across the 2 of their papers we have counts for
3 papers
math.NT2004
Beurling Zeta Functions, Generalised Primes, and Fractal Membranes
T. W. Hilberdink, M. L. Lapidus
We study generalised prime systems with tending to infinity) and the associated Beurling zeta function $ζ_{\mathcal{P}}(s) =\prod_…
math.NT2004★ 11 cited
Fractality, Self-Similarity and Complex Dimensions
Michel L. Lapidus, Machiel van Frankenhuijsen
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric…
math.SP2001
A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation
Michel Lapidus, Machiel van Frankenhuysen
Assuming some regularity of the dynamical zeta function, we establish an explicit formula with an error term for the prime orbit counting function of a suspended flow. We define th…