Addition formulae for Abelian functions associated with specialized curves

J. C. Eilbeck; S. Matsutani; Y. Ônishi

doi:10.1098/rsta.2010.0320

Addition formulae for Abelian functions associated with specialized curves

J. C. Eilbeck, S. Matsutani, Y. Ônishi

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the equianharmonic and lemniscate cases, and in genus 2 we find some new addition formulae for a number of curves. © 2011 The Royal Society.

Original language	English
Pages (from-to)	1245-1263
Number of pages	19
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	369
Issue number	1939
DOIs	https://doi.org/10.1098/rsta.2010.0320
Publication status	Published - 28 Mar 2011

Keywords

Abelian functions
Addition formulae
Sigma functions
Weierstrass functions

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10.1098/rsta.2010.0320

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title = "Addition formulae for Abelian functions associated with specialized curves",

abstract = "We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the equianharmonic and lemniscate cases, and in genus 2 we find some new addition formulae for a number of curves. {\textcopyright} 2011 The Royal Society.",

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AU - Matsutani, S.

AU - Ônishi, Y.

PY - 2011/3/28

Y1 - 2011/3/28

N2 - We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the equianharmonic and lemniscate cases, and in genus 2 we find some new addition formulae for a number of curves. © 2011 The Royal Society.

AB - We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the equianharmonic and lemniscate cases, and in genus 2 we find some new addition formulae for a number of curves. © 2011 The Royal Society.

KW - Abelian functions

KW - Addition formulae

KW - Sigma functions

KW - Weierstrass functions

UR - https://www.scopus.com/pages/publications/79953207668

U2 - 10.1098/rsta.2010.0320

DO - 10.1098/rsta.2010.0320

M3 - Article

SN - 1364-503X

VL - 369

SP - 1245

EP - 1263

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 1939

ER -

Addition formulae for Abelian functions associated with specialized curves

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Keywords

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