Research

Research articles Preprints available at: arXiv: J. D. Lichtman

27. The abc conjecture is true almost always, J. D. Lichtman, submitted, 4 pp.

26. Erdős's integer dilation approximation problem and GCD graphs, D. Koukoulopoulos, Y. Lamzouri, J. D. Lichtman, submitted, 47 pp.

25. Bounds on the exceptional set in the abc conjecture, T. Browning, J. D. Lichtman, J. Teräväinen, submitted, 17 pp.

24. Density theorems for GLn via Rankin-Selberg L-functions, J. D. Lichtman, A. Pascadi, submitted, 24 pp.

23. The Bombieri-Pila determinant method, T. F. Bloom, J. D. Lichtman, Essential Number Theory, 4-2 (2025), 327–348.

22. Primes in arithmetic progressions to large moduli, and Goldbach beyond the square-root barrier,

J. D. Lichtman, appendix with S. Drappeau, submitted, 55 pp.

21. On Erdős sums of almost primes, O. Gorodetsky, J. D. Lichtman, M. D. Wong, Comptes Rendus. Mathématique, 362 (2024), 1571–1596.

20. Higher Mertens constants for almost primes II, J. Bayless, P. Kinlaw, J. D. Lichtman, International Journal of Number Theory, to appear.

19. Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors, J. D. Lichtman, submitted, 27 pp.

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

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

16. Translated sums of primitive sets, J. D. Lichtman, Comptes Rendus. Mathématique, 360 (2022), 409–414.

15. A modification of the linear sieve, and the count of twin primes, J. D. Lichtman, Algebra & Number Theory, 19 (2025), 42 pp.

14. Higher Mertens constants for almost primes, J. Bayless, P. Kinlaw, J. D. Lichtman, Journal of Number Theory, 234 (2022), 448–475.

13. On the critical exponent for k-primitive sets, T. H. Chan, J. D. Lichtman, C. Pomerance, Combinatorica (2021), 19 pp.

12. Averages of the Möbius function on shifted primes, J. D. Lichtman, Quarterly Journal of Mathematics (2021), 1–29.

11. A generalization of primitive sets and a conjecture of Erdős, T. H. Chan, J. D. Lichtman, C. Pomerance, Discrete Analysis 2020:16, 13 pp.

10. Mertens' prime product formula, dissected, J. D. Lichtman, Integers 21A (2021), Ron Graham Memorial Volume, #A17, 15 pp.

9. Almost primes and the Banks-Martin conjecture, J. D. Lichtman, Journal of Number Theory, 211 (2020), 513–529.

8. Primes in prime number races, J. D. Lichtman, G. Martin, C. Pomerance, Proceedings of the American Mathematical Society, 147 (2019), 3743–3757.

7. The Erdős conjecture for primitive sets, J. D. Lichtman, C. Pomerance, Proceedings of the American Mathematical Society, Series B, 6 (2019), 1–14.

6. The reciprocal sum of primitive nondeficient numbers, J. D. Lichtman, Journal of Number Theory, 191 (2018), 104–118.

5. 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.

4. 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.

3. 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.

2. 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.

1. Improved error bounds for the Fermat primality test on random inputs, J. D. Lichtman and C. Pomerance, Mathematics of Computation, 87 (2018), 2871–2890.