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Computational and Analytical Mathematics pp 219–250Cite as

Logarithmic and Complex Constant Term Identities

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 50))

Abstract

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2, p), Adamović and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamović and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove such identities for the root system G2.

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Acknowledgements

The authors have greatly benefited from Tony Guttmann’s and Vivien Challis’ expertise in numerical computations. The authors also thank Antun Milas and the anonymous referee for very helpful remarks, leading to the inclusion of Sect. 11.6.3. OW and WZ are supported by the Australian Research Council.

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia

    Tom Chappell & S. Ole Warnaar

  2. CNRS, Institut Gaspard Monge, Université Paris-Est, Marne-la-Vallée, France

    Alain Lascoux

  3. School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW, 2308, Australia

    Wadim Zudilin

Authors
  1. Tom Chappell
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  2. Alain Lascoux
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  3. S. Ole Warnaar
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  4. Wadim Zudilin
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Corresponding author

Correspondence to Wadim Zudilin .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, USA

    David H. Bailey

  2. Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Heinz H. Bauschke

  3. Dept. Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada

    Peter Borwein

  4. Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

  5. Mathematics and Computer Science, University of Limoges, Limoges, France

    Michel Théra

  6. Mathematics and Computer Science Department, La Sierra University, Riverside, California, USA

    Jon D. Vanderwerff

  7. Dept. Combinatorics & Optimization, University of Waterloo Faculty of Mathematics, Waterloo, Ontario, Canada

    Henry Wolkowicz

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Communicated By David H. Bailey.

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Chappell, T., Lascoux, A., Warnaar, S.O., Zudilin, W. (2013). Logarithmic and Complex Constant Term Identities. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_11

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