Jared Duker Lichtman
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Clarendon Scholar, Oxford (2019-)
Churchill Scholar, Cambridge (2018-19)
Goldwater Scholar, Dartmouth (2017-18)
Byrne Scholar, Dartmouth (2015-18)
Videos
Erdős primitive set conjecture: (3 minute thesis) (CANT talk)
Twin primes & a modified linear sieve: (Webinar talk)
Preprints available at arXiv: J. D. Lichtman
I find it irresistible how subtle patterns emerge from basic multiplication. In my research, I am interested in multiplicative structure broadly interpreted, including primitive sets, multiplicative functions, sieve methods, as well as the primes themselves.
A proof of the Erdős primitive set conjecture, J. D. Lichtman, submitted.
On the Hardy–Littlewood–Chowla conjecture on average, J. D. Lichtman, J. Teräväinen, Forum of Mathematics, Sigma, 10 (2022), 1–17.
Translated sums of primitive sets, J. D. Lichtman, Comptes Rendus. Mathématique, 360 (2022), 409–414.
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, 234 (2022), 448–475.
On the critical exponent for k-primitive sets, T. H. Chan, J. D. Lichtman, C. Pomerance, Combinatorica (2021), 19 pp.
Averages of the Möbius function on shifted primes, J. D. Lichtman, Quarterly Journal of Mathematics (2021), 1–29.
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.