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Dr Bryce Kerr

Associate Lecturer
UNSW Canberra
School of Science

Bryce Kerr is a lecturer whose research lies at the interface of number theory and cryptography. He completed his PhD in 2017 at UNSW Sydney and has held previous appointments at the University of Turku in Finland, the Max Planck Institute for Mathematics in Germany and a DECRA fellowship at UNSW Canberra. 
His research focuses on developing techniques to understand when the output of equations and algorithms look random. These techniques are significant in the context of cryptography, since they allow one to assess the security of cryptosystems and estimate the complexity of algorithms. 
He is a passionate mathematics educator who is committed to fostering an engaging and supportive learning environment that helps students build confidence, develop problem-solving skills, and appreciate the beauty of mathematics.
E-mail
bryce.kerr@unsw.edu.au
Location
School of Science UNSW Canberra
  • Journal articles | 2025
    Bagshaw C; Kerr B, 2025, 'Lattices in function fields and applications', Mathematika, 71, http://dx.doi.org/10.1112/mtk.70010
    Journal articles | 2025
    Bordignon M; Bortolotto C; Kerr B, 2025, 'Weyl sums with multiplicative coefficients and joint equidistribution', Algebra and Number Theory, 19, pp. 1549 - 1580, http://dx.doi.org/10.2140/ant.2025.19.1549
    Journal articles | 2025
    Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2025, 'ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS', Journal of the Institute of Mathematics of Jussieu, 24, pp. 1765 - 1806, http://dx.doi.org/10.1017/S1474748023000397
    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 | 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
    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, 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; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369
    Journal articles | 2020
    Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369
    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
    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
    Journal articles | 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, 6, pp. 1 - 21, 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://arxiv.org/abs/2103.09405v1
    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://arxiv.org/abs/2005.02923v3
    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://arxiv.org/abs/2008.00433v1
    Preprints | 2020
    Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers, http://arxiv.org/abs/2001.03380v4
    Preprints | 2019
    Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2019, Bilinear forms in Weyl sums for modular square roots and applications, http://arxiv.org/abs/1908.10143v3
    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://arxiv.org/abs/1811.09329v1
    Preprints | 2017
    Chang M-C; Kerr B; Shparlinski IE, 2017, On the exponential large sieve inequality for sparse sequences modulo primes, http://arxiv.org/abs/1706.04776v2
    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
    Preprints | 2012
    Kerr B; Shparlinski IE, 2012, On the Distribution of Values and Zeros of Polynomial Systems over Arbitrary Sets, http://arxiv.org/abs/1210.6721v1

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 

My Research Supervision

Riddhi Manna: https://www.unsw.edu.au/hdr/riddhi-manna

Liang Wang: https://www.unsw.edu.au/hdr/liang-wang

Saunak Bhattacharjee: https://www.unsw.edu.au/hdr/saunak-bhattacharjee

Ameya Tilgul: https://www.unsw.edu.au/hdr/ameya-tilgul