Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions

L. K. Mork, Keith Sullivan, Trenton Vogt, Darin J. Ulness
2020 Fractal and Fractional  
This work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level. These theorems then provide a general framework for constructing other lacunary functions that exhibit the same symmetries. These investigations enable one to better explore the effects of the gap behavior on the qualitative features of the associated lacunary functions.
more » ... nary functions. Further, two renormalized products of centered polygonal lacunary functions are defined and a connection to Ramanunjan's triangular lacunary series is made via several theorems.
doi:10.3390/fractalfract4020024 fatcat:qmktslmujrch3n6wyftigiocpm