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Littlewood Polynomials

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Analytic Number Theory, Modular Forms and q-Hypergeometric Series (ALLADI60 2016)

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Abstract

We consider exponential polynomials with restricted coefficients, for example by requiring that they all have absolute value 1, or the even more restricted class considered by Littlewood, namely those whose coefficients are all \(\pm 1\). This paper expands on material presented in the Erdős Colloquium delivered on March 18, 2016, as part of the 2016 Gainesville International Number Theory Conference.

This paper is dedicated to Krishnaswami Alladi on the occasion of his 60th birthday

Research supported in part by NSF grant DMS-063529.

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Acknowledgements

The author is also indebted to the referee for valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109–1043, USA

    Hugh L. Montgomery

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  1. Hugh L. Montgomery
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Correspondence to Hugh L. Montgomery .

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Editors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, State College, Pennsylvania, USA

    George E. Andrews

  2. Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

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Montgomery, H.L. (2017). Littlewood Polynomials. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_30

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