Status:
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:
Recent work on the Erdős primitive set conjecture
Preprints available on arXiv: J. D. Lichtman
Prizes, awards, and scholarships:
Clarendon Scholar, Oxford (2019-)
Churchill Scholar, Cambridge (2018-19)
Major / recent publications:
On the critical exponent for k-primitive sets, T. H. Chan, J. D. Lichtman, C. Pomerance, submitted.
Averages of the Möbius function on shifted primes, J. D. Lichtman, submitted.
Mertens' prime product formula, dissected, J. D. Lichtman, submitted.
A generalization of primitive sets and a conjecture of Erdős, T. H. Chan, J. D. Lichtman, C. Pomerance, Discrete Analysis 2020:16, 13 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 Fourier 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, submitted.
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.