Higher dimensional modular equations of degree 7 (Q2707576)

In this note the author considers Thetanullwerte with half integral characteristics \(\theta[m] (\tau|0)\). He studies, in all degree relations between \(\theta[m] (\tau|0)\) and \(\theta[m] (n\tau|0)\theta[m] (\tau|0)\), \(n\) a positive integer. First he recalls some higher dimensional modular equation of degree 3 that was found in 1860, then, using a nice product formula for theta functions given by \textit{S. Koizumi} [Math. Ann. 242, 127-145 (1979; Zbl 0404.14017)], proves a higher dimensional modular equation of degree \(7\).NEWLINENEWLINEFor the entire collection see [Zbl 0932.00040].