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.
The theory of elliptic integrals and elliptic functions, which were driving force of mathematics in the eighteenth and nineteents centuries, are not only beautiful but have many applications in mathematics and physics. This simple reader-friendly book, based on the lectures at the Faculty of Mathematics, HSE, explains such theory and applications in original way.