# Jared Duker Lichtman

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

**Primes in arithmetic progressions to large moduli, and Goldbach beyond the square-root barrier,** J. D. Lichtman, submitted. Appendix with S. Drappeau.

**On Erdős sums of almost primes,** O. Gorodetsky, J. D. Lichtman, M. D. Wong, submitted.

**Higher Mertens constants for almost primes II**, J. Bayless, P. Kinlaw, J. D. Lichtman, submitted.

**Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors,** J. D. Lichtman, submitted.

**A proof of the Erdős primitive set conjecture,** J. D. Lichtman, *Forum of Mathematics, Pi,* 11 (2023) 22 pp.

**On the Hardy–Littlewood–Chowla conjecture on average**, J. D. Lichtman, J. Teräväinen, *Forum of Mathematics, Sigma*, 10 (2022), 17 pp.

**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.

I find it irresistible how subtle patterns emerge from basic multiplication. In my research, I am interested in the prime numbers as well as related multiplicative structure, broadly interpreted.

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) (NT Web Seminar talk)

Twin primes & a modified linear sieve: (Webinar talk)

*Preprints available* at arXiv: J. D. Lichtman