Finiteness property for generalized abelian integrals

Rémi Soufflet[1]

  • [1] Institute of Mathematics UJ, ul. Reymonta 4, 30-059 Kraków (Pologne)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 3, page 767-785
  • ISSN: 0373-0956

Abstract

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We study the integrals of real functions which are finite compositions of globally subanalytic maps and real power functions. These functions have finiteness properties very similar to those of subanalytic functions. Our aim is to investigate how such finiteness properties can remain when taking the integrals of such functions. The main result is that for almost all power maps arising in a x λ -function, its integration leads to a non-oscillating function. This can be seen as a generalization of Varchenko and Khovanskii’s finiteness theorems for abelian integrals.

How to cite

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Soufflet, Rémi. "Finiteness property for generalized abelian integrals." Annales de l’institut Fourier 53.3 (2003): 767-785. <http://eudml.org/doc/116052>.

@article{Soufflet2003,
abstract = {We study the integrals of real functions which are finite compositions of globally subanalytic maps and real power functions. These functions have finiteness properties very similar to those of subanalytic functions. Our aim is to investigate how such finiteness properties can remain when taking the integrals of such functions. The main result is that for almost all power maps arising in a $x^\lambda $-function, its integration leads to a non-oscillating function. This can be seen as a generalization of Varchenko and Khovanskii’s finiteness theorems for abelian integrals.},
affiliation = {Institute of Mathematics UJ, ul. Reymonta 4, 30-059 Kraków (Pologne)},
author = {Soufflet, Rémi},
journal = {Annales de l’institut Fourier},
keywords = {abelian integrals; preparation theorem; o-minimal structures; diophantine conditions; Diophantine conditions},
language = {eng},
number = {3},
pages = {767-785},
publisher = {Association des Annales de l'Institut Fourier},
title = {Finiteness property for generalized abelian integrals},
url = {http://eudml.org/doc/116052},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Soufflet, Rémi
TI - Finiteness property for generalized abelian integrals
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 3
SP - 767
EP - 785
AB - We study the integrals of real functions which are finite compositions of globally subanalytic maps and real power functions. These functions have finiteness properties very similar to those of subanalytic functions. Our aim is to investigate how such finiteness properties can remain when taking the integrals of such functions. The main result is that for almost all power maps arising in a $x^\lambda $-function, its integration leads to a non-oscillating function. This can be seen as a generalization of Varchenko and Khovanskii’s finiteness theorems for abelian integrals.
LA - eng
KW - abelian integrals; preparation theorem; o-minimal structures; diophantine conditions; Diophantine conditions
UR - http://eudml.org/doc/116052
ER -

References

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