Indefinite zeta functions

Abstract We define generalised zeta functions associated with indefinite quadratic forms of signature $$(g-1,1)$$ (g-1,1) —and more generally, to complex symmetric matrices whose imaginary part has we investigate their properties. These are defined as Mellin transforms theta in the sense Zwegers, which turn Siegel modular setting. prove an analytic continuation and functional equation for functions. also show that dimension 2 specialise differences ray class real fields, leading Taylor coefficients at $$s=0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">s=0 predicted be logarithms algebraic units by Stark conjectures.