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EXPONENTIAL SUMS AND ADDITIVE COMBINATORICS

Part of: Exponential sums and character sums Finite fields and commutative rings (number-theoretic aspects) Sequences and sets

Published online by Cambridge University Press:  09 November 2020

SIMON MACOURT Open the ORCID record for SIMON MACOURT [Opens in a new window]
SIMON MACOURT*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Kensington NSW 2052, Australia
*
e-mail: s.macourt@unsw.edu.au
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Abstract

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Keywords

exponential sumadditive combinatoricsfinite fieldsparse polynomial

MSC classification

Primary: 11B30: Arithmetic combinatorics; higher degree uniformity
Secondary: 11L07: Estimates on exponential sums 11T23: Exponential sums 11T30: Structure theory
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 506 - 508
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to the University of New South Wales in January 2020: degree approved on 26 March 2020; supervisor Igor Shparlinski.

References

Kerr, B. and Macourt, S., ‘Multilinear exponential sums with a general class of weights’, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear.Google Scholar
Macourt, S., ‘Bounds on exponential sums with quadrinomials’, J. Number Theory 193 (2018), 118–127.CrossRefGoogle Scholar
Macourt, S., ‘Incidence results and bounds of trilinear and quadrilinear exponential sums’, SIAM J. Discrete Math. 32(2) (2018), 815–825.CrossRefGoogle Scholar
Macourt, S., ‘Decomposition of subsets of finite fields’, Funct. Approx. Comment. Math. 61(2) (2019), 243–255.CrossRefGoogle Scholar
Macourt, S., Shkredov, I. D. and Shparlinski, I. E., ‘Multiplicative energy of shifted subgroups and bounds on exponential sums with trinomials in finite fields’, Canad. J. Math. 70(6) (2018), 1319–1338.10.4153/CJM-2017-044-2CrossRefGoogle Scholar