Twisted Maaß-Koecher series and spinor zeta functions

Abstract

It is shown that a Siegel-Hecke eigenform of integral weight $k$ and genus 2 is uniquely determined by its Fourier coefficients indexed by $nT$ where $T$ runs over all half-integral positive definite primitive matrices of size 2 and $n$ over all squarefree positive integers. The proof uses analytic arguments involving Koecher-Maaß series and spinor zeta functions.