Bryce Kerr

DECRA
Research Fellow

PhD Study Opportunities

Are you interested in Graduate Research?  Explore some of the PhD Study Opportunities at UNSW Canberra.  We offer a diverse range of Scholarships Opportunities to domestic and international students to suit you and your situation.

Scholarships of $35,000 (AUD) are available for PhD applicants who achieved H1 (High Distinction) in their undergraduate program and/or have completed a Masters by Research.

PUBLICATIONS
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Preprints
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Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, Energy bounds for modular roots and their applications, http://dx.doi.org/10.48550/arxiv.2103.09405
2021
Kerr B; Mello J; Shparlinski I, 2020, An effective local-global principle for algebraic varieties and the sum product problem in finite fields, http://dx.doi.org/10.48550/arxiv.2005.02923
2020
Kerr B; Mello J; Shparlinski IE, 2020, On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields
2020
Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers, http://dx.doi.org/10.48550/arxiv.2001.03380
2020
Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2019, Bilinear forms in Weyl sums for modular square roots and applications
2019
Kerr B; Shparlinski IE, 2018, Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions
2018
Kerr B; Shparlinski IE; Yau KH, 2017, A refinement of the Burgess bound for character sums
2017
Chang M-C; Kerr B; Shparlinski IE, 2017, On the exponential large sieve inequality for sparse sequences modulo primes
2017
Journal articles
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Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, vol. 385, pp. 309 - 355, http://dx.doi.org/10.1007/s00208-021-02352-x
2023
Kerr B; Macourt S, 2021, 'Multilinear exponential sums with a general class of weights', Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 22, pp. 1105 - 1130, http://dx.doi.org/10.2422/2036-2145.201908_017
2021
Kerr B; Mohammadi A, 2021, 'Points on polynomial curves in small boxes modulo an integer', Journal of Number Theory, vol. 223, pp. 64 - 78, http://dx.doi.org/10.1016/j.jnt.2020.11.006
2021
Kerr B, 2021, 'Bounds of Multiplicative Character Sums over Shifted Primes', Proceedings of the Steklov Institute of Mathematics, vol. 314, pp. 64 - 89, http://dx.doi.org/10.1134/S0081543821040040
2021
Kerr B, 2021, 'Some multiplicative equations in finite fields', Finite Fields and their Applications, vol. 75, http://dx.doi.org/10.1016/j.ffa.2021.101883
2021
Kerr B; Mello J; Shparlinski IE, 2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, vol. 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478
2021
Kerr B; Mérai L; Shparlinski I, 2021, 'On digits of Mersenne numbers', Revista Matemática Iberoamericana, vol. 38, pp. 1901 - 1925, http://dx.doi.org/10.4171/rmi/1316
2021
Bordignon M; Kerr B, 2020, 'An explicit pólya-vinogradov inequality via partial Gaussian sums', Transactions of the American Mathematical Society, vol. 373, pp. 6503 - 6527, http://dx.doi.org/10.1090/tran/8138
2020
Shparlinski I; Kerr B, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, pp. 1 - 21, http://dx.doi.org/10.1007/s40993-020-0191-9
2020
Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, vol. 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737
2020
Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, vol. 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369
2020
Kerr B; Shparlinski IE, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, vol. 6, http://dx.doi.org/10.1007/s40993-020-0191-9
2020
Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, vol. 375, http://dx.doi.org/10.1016/j.aim.2020.107369
2020
Kerr B, 2020, 'On the constant in the Pólya-Vinogradov inequality', Journal of Number Theory, vol. 212, pp. 265 - 284, http://dx.doi.org/10.1016/j.jnt.2019.11.003
2020
Kerr B; McGown KJ; Trudgian T, 2020, 'The least primitive root modulo p2', Journal of Number Theory, vol. 215, pp. 20 - 27, http://dx.doi.org/10.1016/j.jnt.2020.01.002
2020
Chen C; Kerr B; Mohammadi ALI, 2019, 'A new sum-product estimate in prime fields', Bulletin of the Australian Mathematical Society, vol. 100, pp. 268 - 280, http://dx.doi.org/10.1017/S0004972719000303
2019
Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, vol. 459, pp. 53 - 81, http://dx.doi.org/10.1016/j.jmaa.2017.10.070
2018
Kerr B, 2018, 'Incomplete gauss sums modulo primes', Quarterly Journal of Mathematics, vol. 69, pp. 729 - 745, http://dx.doi.org/10.1093/qmath/hax059
2018
Kerr B, 2017, 'On the congruence x1x2≡x3x4modq', Journal of Number Theory, vol. 180, pp. 154 - 168, http://dx.doi.org/10.1016/j.jnt.2017.02.012
2017
Kerr B, 2015, 'Lower bounds for the Riemann zeta function on short intervals of the critical line', Archiv der Mathematik, vol. 105, pp. 45 - 53, http://dx.doi.org/10.1007/s00013-015-0777-y
2015
Kerr B, 2015, 'Incomplete exponential sums over exponential functions', Quarterly Journal of Mathematics, vol. 66, pp. 213 - 224, http://dx.doi.org/10.1093/qmath/hau015
2015
Chang MC; Kerr B; Shparlinski IE; Zannier U, 2014, 'Elements of large order on varieties over prime finite fields', Journal de Theorie des Nombres de Bordeaux, vol. 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880
2014
Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, vol. 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012
2013
Kerr B, 2013, 'Solutions to polynomial congruences in well-shaped sets', Bulletin of the Australian Mathematical Society, vol. 88, pp. 435 - 447, http://dx.doi.org/10.1017/S0004972713000324
2013
Working Papers
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Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, Michigan Mathematical Journal, http://dx.doi.org10.1307/mmj/1573700737, http://arxiv.org/abs/1711.10582v1
2020

GRANTS
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DE220100859: https://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DE220100859

Organisational units
lensSchool of Science
Sub Theme
lensNumber Theory