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Mat. Zametki, 2018, Volume 103, Issue 2, Pages 236–247 (Mi mz11423)  

Hirzebruch Functional Equations and Krichever Complex Genera

I. V. Netayab

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics" (HSE), Moscow

Abstract: 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 $n$.

Keywords: Hirzebruch genus, elliptic function, functional equation.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
This work was supported by the Russian Science Foundation under grant 14-50-00150, RSF IPPI.


DOI: https://doi.org/10.4213/mzm11423

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English version:
Mathematical Notes, 2018, 103:2, 232–242

Bibliographic databases:

Document Type: Article
UDC: 515.14
Received: 21.10.2016
Revised: 14.04.2017

Citation: I. V. Netay, “Hirzebruch Functional Equations and Krichever Complex Genera”, Mat. Zametki, 103:2 (2018), 236–247; Math. Notes, 103:2 (2018), 232–242

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