Status:
+44 1865 283891
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
I find it irresistible how subtle patterns emerge from basic multiplication. In my research, I am interested in multiplicative structure broadly interpreted, e.g. smooth numbers, primitive sets, multiplicative functions, sieve methods, as well as the primes themselves.
Further details:
Webinar talk: Twin primes & a modified linear sieve
Oxford case study: Erdős primitive set conjecture
Preprints available at arXiv: J. D. Lichtman
Prizes, awards, and scholarships:
Clarendon Scholar, Oxford (2019-)
Churchill Scholar, Cambridge (2018-19)
Major / recent publications:
On the Hardy–Littlewood–Chowla conjecture on average, J. D. Lichtman, J. Teräväinen, submitted.
Translated sums of primitive sets, J. D. Lichtman, Comptes Rendus. Mathématique, to appear.
A modification of the linear sieve, and the count of twin primes, J. D. Lichtman, submitted.
Higher Mertens constants for almost primes, J. Bayless, P. Kinlaw, J. D. Lichtman, Journal of Number Theory, to appear.
On the critical exponent for k-primitive sets, T. H. Chan, J. D. Lichtman, C. Pomerance, Combinatorica, to appear.
Averages of the Möbius function on shifted primes, J. D. Lichtman, Quarterly Journal of Mathematics, to appear.
A generalization of primitive sets and a conjecture of Erdős, T. H. Chan, J. D. Lichtman, C. Pomerance, Discrete Analysis 2020:16, 13 pp.
Mertens' prime product formula, dissected, J. D. Lichtman, Integers 21A (2021), Ron Graham Memorial Volume, #A17, 15 pp.
Almost primes and the Banks-Martin conjecture, J. D. Lichtman, Journal of Number Theory, 211 (2020), 513-529.
Primes in prime number races, J. D. Lichtman, G. Martin, and C. Pomerance, Proceedings of the American Mathematical Society, 147 (2019), 3743-3757.
The Erdős conjecture for primitive sets, J. D. Lichtman and C. Pomerance, Proceedings of the American Mathematical Society, Series B, 6 (2019), 1-14.
The reciprocal sum of primitive nondeficient numbers, J. D. Lichtman, Journal of Number Theory, 191 (2018), 104-118.
A refined conjecture for the variance of Gaussian primes across sectors, R. Chen, Y. H. Kim, J. D. Lichtman, S. J. Miller, S. Sweitzer, E. Waxman, E. Winsor, J. Yang, Experimental Mathematics (2020), 1-21.
Lower-order biases in the second moment of Dirichlet coefficients in families of L-functions, M. Asada, R. Chen, E. Fourakis, Y. Kim, A. Kwon, J. D. Lichtman, B. Mackall, S. J. Miller, E. Waxman, E. Winsor, K. Winsor, J. Yang, K. Yang, Experimental Mathematics (2021), 1-27.
Spectral statistics of non-Hermitian matrix ensembles, R. Chen, Y. H. Kim, J. D. Lichtman, S. J. Miller, S. Sweitzer, E. Winsor, Random Matrices: Theory and Applications, 8 (2019), 1-40.
Explicit estimates for the distribution of numbers free of large prime factors, J. D. Lichtman and C. Pomerance, Journal of Number Theory, 183 (2018), 1-23.
Improved error bounds for the Fermat primality test on random inputs, J. D. Lichtman and C. Pomerance, Mathematics of Computation, 87 (2018), 2871-2890.