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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The holomorphy conjecture for ideals in dimension two
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by Ann Lemahieu and Lise Van Proeyen PDF
Proc. Amer. Math. Soc. 139 (2011), 3845-3852 Request permission

Abstract:

The holomorphy conjecture predicts that the topological zeta function associated to a polynomial $f \in \mathbb {C}[x_1,\ldots ,x_n]$ and an integer $d > 0$ is holomorphic unless $d$ divides the order of an eigenvalue of local monodromy of $f$. In this paper, we generalise the holomorphy conjecture to the setting of arbitrary ideals in $\mathbb {C}[x_1,\ldots ,x_n]$, and we prove it when $n=2$.
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Additional Information
  • Ann Lemahieu
  • Affiliation: Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
  • Address at time of publication: Université Lille 1, UFR de Mathématiques, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
  • Email: lemahieu.ann@gmail.com
  • Lise Van Proeyen
  • Affiliation: Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
  • Email: lisevanproeyen@gmail.com
  • Received by editor(s): May 16, 2008
  • Received by editor(s) in revised form: May 6, 2009, and September 18, 2010
  • Published electronically: June 29, 2011
  • Additional Notes: This research was partially supported by the Fund of Scientific Research - Flanders (G.0318.06) and MEC PN I+D+I MTM2007-64704.
  • Communicated by: Ted Chinburg
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3845-3852
  • MSC (2010): Primary 14-XX
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11186-9
  • MathSciNet review: 2823031