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Structured Hadamard Conjecture

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Number Theory and Related Fields

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 43))

Abstract

We present three different formalisms for a structured version of the Hadamard conjecture. Two of these formalisms are new, and we use them to provide independent verifications of some of the previously known computational results on this structured version of the Hadamard conjecture.

Étant donné un déterminant \(\displaystyle{\Delta = \left\vert \begin{array}{cccc} a_{1} & b_{1} & \ldots & \ell_{1} \\ a_{2} & b_{2} & \ldots & \ell_{2}\\ \ldots & \ldots & \ldots & \ldots \\ a_{n}&b_{n}&\ldots &\ell_{n}\\ \end{array} \right\vert }\) dans lequel on sait que les éléments sont inférieurs en valeur absolue à une quantité déterminée A, il y a souvent lieu de chercher une limite que le module de Δ ne puisse dépasser.

– Jacques Hadamard, 1893

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Acknowledgements

The author is grateful to the anonymous referees for their careful scrutiny of the original submission and their constructive and pertinent comments that led to a significantly improved version of this paper.

This work is supported by an NSERC grant.

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Authors and Affiliations

  1. Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, Canada, N2L 3C5

    Ilias S. Kotsireas

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  1. Ilias S. Kotsireas
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Correspondence to Ilias S. Kotsireas .

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Editors and Affiliations

  1. , School of Math. & Physical Sciences, University of Newcastle, Callaghan, 2308, Australia

    Jonathan M. Borwein

  2. , Department of Computing, Macquarie University, Herring Road, North Ryde, 2109, New South Wales, Australia

    Igor Shparlinski

  3. , School of Math. & Physical Sciences, University of Newcastle, Callaghan, 2308, Australia

    Wadim Zudilin

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Kotsireas, I.S. (2013). Structured Hadamard Conjecture. In: Borwein, J., Shparlinski, I., Zudilin, W. (eds) Number Theory and Related Fields. Springer Proceedings in Mathematics & Statistics, vol 43. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6642-0_11

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