Hirzebruch Functional Equations and Krichever Complex Genera

As is well known, the two-parameter Todd genus and the elliptic functions of level $d$ define $n$-multiplicative Hirzebruch genera if $d$ divides $n+ 1$. Both cases are special cases of the Krichever genera defined by the Baker–Akhiezer function. In the present paper, the inverse problem is solved. Namely, it is proved that only these properties define $n$-multiplicative Hirzebruch genera among all Krichever genera for all $n$.