4 papers · 1 filter
Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike
Peter J. Grabner
Extremal quasimodular forms have been introduced by M.~Kaneko and M.Koike as as quasimodular forms which have maximal possible order of vanishing at . We show an asymptoti…
Quasimodular forms as solutions of Modular differential equations
Peter J. Grabner
We study quasimodular forms of depth and determine under which conditions they occur as solutions of modular differential equations. Furthermore, we study which modular dif…
Poissonian pair correlation on manifolds via the heat kernel
Peter J. Grabner, Tetiana A. Stepanyuk
We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earl…
Redundancy of minimal weight expansions in Pisot bases
Peter J. Grabner, Wolfgang Steiner
Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer as a sum , where the digits are…