Interlacing properties for zeros of a family of modular forms

Abstract

Getz presented a family of level one modular forms [Formula: see text] for which all zeros lie on the unit circle in the fundamental domain. Expanding on work from Nozaki, Griffin et al., and Saha and Saradha, we show that the non-elliptic zeros of these [Formula: see text] satisfy two interlacing properties: standard interlacing, where the zeros of [Formula: see text] and [Formula: see text] alternate if and only if [Formula: see text] for sufficiently large [Formula: see text]; and Stieltjes interlacing, where for [Formula: see text] large enough, between any two zeros of [Formula: see text], there is a zero of [Formula: see text].