Mora, Gaspar, Sepulcre, Juan Matias, Vidal, Tomás
On the existence of exponential polynomials with prefixed gaps
Bulletin of the London Mathematical Society. 2013, 45(6): 1148-1162. doi:10.1112/blms/bdt043
URI: http://hdl.handle.net/10045/38408
DOI: 10.1112/blms/bdt043
ISSN: 0024-6093 (Print)
Abstract: 
This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.
Keywords:Functions of a complex variable, Entire functions, Fractals
London Mathematical Society
info:eu-repo/semantics/article