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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 4, Pages 1–17 (Mi faa3219)  

This article is cited in 3 scientific papers (total in 3 papers)

Hirzebruch Functional Equation and Elliptic Functions of Level $d$

V. M. Buchstaber, I. V. Netay

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: A function $f(x)$ of a complex variable $x$ regular in a neighborhood of $x=0$ and such that $f(0)=0$ and $f'(0)=1$ is said to be $n$-rigid if the sum of residues of the function $\prod_{i=0}^n1/f(x-x_i)$ does not depend on the choice of different points $x_0,…,x_n$ in a small neighborhood of $x=0$. The power series expansion of an $n$-rigid function is determined by a functional equation. We refer to this equation as the Hirzebruch $n$-equation. If $d$ is a divisor of $n+1$, then any elliptic function of level $d$ is $n$-rigid. A description of the manifold of all $2$-rigid functions has been obtained very recently. The main result of this work is a description of the manifold of all $3$-rigid functions.

Keywords: functional equation, Hirzebruch genus, elliptic function

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


DOI: https://doi.org/10.4213/faa3219

Full text: PDF file (245 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:4, 239–252

Bibliographic databases:

Document Type: Article
UDC: 517.9+515.178.13+515.14
Received: 05.10.2015

Citation: V. M. Buchstaber, I. V. Netay, “Hirzebruch Functional Equation and Elliptic Functions of Level $d$”, Funktsional. Anal. i Prilozhen., 49:4 (2015), 1–17; Funct. Anal. Appl., 49:4 (2015), 239–252

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. Yu. Bunkova, “Elliptic function of level $4$”, Proc. Steklov Inst. Math., 294 (2016), 201–214  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. I. V. Netay, “Hirzebruch Functional Equations and Krichever Complex Genera”, Math. Notes, 103:2 (2018), 232–242  mathnet  crossref  crossref  isi  elib
    3. Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47  mathnet  crossref  crossref  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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