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Dr Bryce Kerr

Research Fellow
UNSW Canberra
School of Science
E-mail
bryce.kerr@unsw.edu.au
Location
School of Science UNSW Canberra
  • Journal articles | 2024
    Kerr B; Mello J; Shparlinski IE, 2024, 'An effective local-global principle and additive combinatorics in finite fields', Journal d'Analyse Mathematique, 152, pp. 109 - 135, http://dx.doi.org/10.1007/s11854-023-0291-2
    Journal articles | 2024
    Kerr B; Mohammad A; Shparlinski IE, 2024, 'ADDITIVE ENERGY OF POLYNOMIAL IMAGES', SIAM Journal on Discrete Mathematics, 38, pp. 2163 - 2180, http://dx.doi.org/10.1137/23M1582941
    Journal articles | 2024
    Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2024, 'ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS', Journal of the Institute of Mathematics of Jussieu, http://dx.doi.org/10.1017/S1474748023000397
    Journal articles | 2023
    Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, 385, pp. 309 - 355, http://dx.doi.org/10.1007/s00208-021-02352-x
    Journal articles | 2023
    Kerr B; Shparlinski IE; Wu X; Xi P, 2023, 'Bounds on bilinear forms with Kloosterman sums', Journal of the London Mathematical Society, 108, pp. 578 - 621, http://dx.doi.org/10.1112/jlms.12753
    Journal articles | 2022
    Kerr B; Mérai L; Shparlinski IE, 2022, 'On digits of Mersenne numbers', Revista Matematica Iberoamericana, 38, pp. 1901 - 1925, http://dx.doi.org/10.4171/RMI/1316
    Journal articles | 2021
    Kerr B; Macourt S, 2021, 'Multilinear exponential sums with a general class of weights', Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 22, pp. 1105 - 1130, http://dx.doi.org/10.2422/2036-2145.201908_017
    Journal articles | 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, 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478
    Journal articles | 2021
    Kerr B; Mohammadi A, 2021, 'Points on polynomial curves in small boxes modulo an integer', Journal of Number Theory, 223, pp. 64 - 78, http://dx.doi.org/10.1016/j.jnt.2020.11.006
    Journal articles | 2021
    Kerr B, 2021, 'Bounds of Multiplicative Character Sums over Shifted Primes', Proceedings of the Steklov Institute of Mathematics, 314, pp. 64 - 89, http://dx.doi.org/10.1134/S0081543821040040
    Journal articles | 2021
    Kerr B, 2021, 'Some multiplicative equations in finite fields', Finite Fields and their Applications, 75, http://dx.doi.org/10.1016/j.ffa.2021.101883
    Journal articles | 2020
    Bordignon M; Kerr B, 2020, 'An explicit pólya-vinogradov inequality via partial Gaussian sums', Transactions of the American Mathematical Society, 373, pp. 6503 - 6527, http://dx.doi.org/10.1090/tran/8138
    Journal articles | 2020
    Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, http://dx.doi.org/10.1016/j.aim.2020.107369
    Journal articles | 2020
    Kerr B; McGown KJ; Trudgian T, 2020, 'The least primitive root modulo p2', Journal of Number Theory, 215, pp. 20 - 27, http://dx.doi.org/10.1016/j.jnt.2020.01.002
    Journal articles | 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, 6, http://dx.doi.org/10.1007/s40993-020-0191-9
    Journal articles | 2020
    Kerr B, 2020, 'On the constant in the Pólya-Vinogradov inequality', Journal of Number Theory, 212, pp. 265 - 284, http://dx.doi.org/10.1016/j.jnt.2019.11.003
    Journal articles | 2020
    Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737
    Journal articles | 2020
    2020, 'Bilinear forms in Weyl sums for modular square roots and applications', , http://dx.doi.org/10.1016/j.aim.2020.107369
    Journal articles | 2020
    2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', , http://dx.doi.org/10.1007/s40993-020-0191-9
    Journal articles | 2019
    Chen C; Kerr B; Mohammadi ALI, 2019, 'A new sum-product estimate in prime fields', Bulletin of the Australian Mathematical Society, 100, pp. 268 - 280, http://dx.doi.org/10.1017/S0004972719000303
    Journal articles | 2018
    Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, 459, pp. 53 - 81, http://dx.doi.org/10.1016/j.jmaa.2017.10.070
    Journal articles | 2018
    Kerr B, 2018, 'Incomplete gauss sums modulo primes', Quarterly Journal of Mathematics, 69, pp. 729 - 745, http://dx.doi.org/10.1093/qmath/hax059
    Journal articles | 2017
    Kerr B, 2017, 'On the congruence x1x2≡x3x4modq', Journal of Number Theory, 180, pp. 154 - 168, http://dx.doi.org/10.1016/j.jnt.2017.02.012
    Journal articles | 2015
    Kerr B, 2015, 'Incomplete exponential sums over exponential functions', Quarterly Journal of Mathematics, 66, pp. 213 - 224, http://dx.doi.org/10.1093/qmath/hau015
    Journal articles | 2015
    Kerr B, 2015, 'Lower bounds for the Riemann zeta function on short intervals of the critical line', Archiv der Mathematik, 105, pp. 45 - 53, http://dx.doi.org/10.1007/s00013-015-0777-y
    Journal articles | 2014
    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, 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880
    Journal articles | 2013
    Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012
    Journal articles | 2013
    Kerr B, 2013, 'Solutions to polynomial congruences in well-shaped sets', Bulletin of the Australian Mathematical Society, 88, pp. 435 - 447, http://dx.doi.org/10.1017/S0004972713000324
  • Working Papers | 2020
    Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, http://dx.doi.org10.1307/mmj/1573700737
  • Preprints | 2021
    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
    Preprints | 2020
    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
    Preprints | 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, , http://dx.doi.org/10.48550/arxiv.2008.00433
    Preprints | 2020
    Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers, , http://dx.doi.org/10.48550/arxiv.2001.03380
    Preprints | 2019
    Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2019, Bilinear forms in Weyl sums for modular square roots and applications, , http://dx.doi.org/10.48550/arxiv.1908.10143
    Preprints | 2018
    Kerr B; Shparlinski IE, 2018, Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions, , http://dx.doi.org/10.48550/arxiv.1811.09329
    Preprints | 2017
    Chang M-C; Kerr B; Shparlinski IE, 2017, On the exponential large sieve inequality for sparse sequences modulo primes, , http://dx.doi.org/10.48550/arxiv.1706.04776
    Preprints | 2017
    Kerr B; Shparlinski IE; Yau KH, 2017, A refinement of the Burgess bound for character sums, , http://dx.doi.org/10.48550/arxiv.1711.10582

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

DP230100534: https://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DP230100534

Analytic number theory, geometry of numbers, additive combinatorics.

We offer PhD programs in mathematics and statistics and actively encourage new applications. Scholarships of $35,000 (AUD) are available for PhD applicants who achieved H1 (High Distinction) in their undergraduate program and have completed a Master by Research. If you are interested in applying, please contact bryce.kerr@unsw.edu.au