Steven Charlton

In preparation

Preprints

  1. A review of Dan's reduction method for multiple polylogarithms (Historical) Mathematica worksheets to verify the results 1703.03961 [math.NT]
  2. Appendix A in Complete families of embedded high genus CMC surfaces in the 3-sphere (Superseded by 2411.15071 [math.DG]) L. Heller, S. Heller and M. Traizet 2108.10214 [math.DG]
  3. Differential operators and a depth reduction for the alternating multiple zeta values \(\zeta(1, \ldots, 1, \overline{2m})\) K. C. Au and M. E. Hoffman 2312.17148 [math.NT]
  4. Creative telescoping and generating functions of (variants of) multiple zeta values K. C. Au 2404.16199 [math.NT]
  5. Symmetries of weight 6 multiple polylogarithms and Goncharov's Depth Conjecture 2405.13853 [math.NT]
  6. Minimal surfaces and alternating multiple zetas L. Heller, S. Heller and M. Traizet 2411.15071 [math.DG]
  7. Euler-Kronecker constants of modular forms: beyond Dirichlet \(L\)-series A. Medvedovsky and P. Moree 2412.01803 [math.NT]
  8. Multiple polylogarithms and the Steinberg module D. Radchenko and D. Rudenko 2505.02202 [math.NT]
  9. An explicit Galois descent for multiple \(t\)-values of maximal height M. E. Hoffman and N. Sato 2605.10262 [math.NT]
  10. Multiple zeta values ending with a fixed string 2606.09544 [math.NT]
  11. On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials B. Heim and J. Stumpenhusen 2606.09545 [math.NT]

Publications

  1. \( \zeta(\{ \, \{2\}^m, 1, \{2\}^m, 3 \}^n, \{2\}^m) / \pi^{4n + 2m(2n+1)} \) is rational Journal of Number Theory 148 (2015), pp. 463-477 1306.6775 [math.NT] 10.1016/j.jnt.2014.09.028
  2. Generalized Jacobi-Trudi determinants and evaluations of Schur multiple zeta values H. Bachmann European Journal of Combinatorics 87 (2020), pp. 103-133 1908.05061 [math.NT] 10.1016/j.ejc.2020.103133
  3. An analogue of cyclic insertion for mutiple zeta star values Kyushu Journal of Mathematics 74 (2020), pp. 337-352 1806.10053 [math.NT] 10.2206/kyushujm.74.337
  4. On functional equations for Nielsen polylogarithms H. Gangl and D. Radchenko Communications in Number Theory and Physics, Vol. 15, No. 2 (2021), pp. 363-454 1908.04770 [math.NT] 10.4310/CNTP.2021.v15.n2.a4
  5. The alternating block decomposition of iterated integrals, and cyclic insertion on multiple zeta values The Quarterly Journal of Mathematics, Volume 72, Issue 3, September 2021, Pages 975–1028 1703.03784 [math.NT] 10.1093/qmath/haaa056
  6. Clean single-valued polylogarithms C. Duhr and H. Gangl SIGMA 17 (2021), 107, 34 pages, Special Issue on Algebraic Structures in Perturbative Quantum Field Theory in honor of Dirk Kreimer for his 60th birthday. 2104.04344 [math.NT] 10.3842/SIGMA.2021.107
  7. Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7 H. Gangl and D. Radchenko Pure and Applied Mathematics Quarterly, Vol. 19, No. 1 (2023), pp. 85-93 (Special issue in honor of Don Zagier.) 2012.09840 [math.NT] 10.4310/PAMQ.2023.v19.n1.a5
  8. On two conjectures of Sun concerning Apéry-like series H. Gangl, L. Lai, C. Xu, and J. Zhao Forum Mathematicum, Volume 35 Issue 6 (2023), pp. 1533-1547 2210.14704 [math.NT] 10.1515/forum-2022-0325
  9. On the Goncharov depth conjecture and polylogarithms of depth two H. Gangl, D. Radchenko, and D. Rudenko Selecta Mathematica New Series, Vol. 30, #27 (2024) 2210.11938 [math.NT] 10.1007/s00029-024-00918-6
  10. Evaluation of the multiple zeta values \(\zeta(2,\ldots,2,4,2,\ldots,2) \) and period polynomial relations A. Keilthy Forum of Mathematics, Sigma, Vol 12. #e46 (2024) 2210.03616 [math.NT] 10.1017/fms.2024.16
  11. On the evaluation of the alternating multiple \( t \) value \( t(\overline{1},\ldots,\overline{1}, 1, \overline{1},\ldots,\overline{1}) \) The Ramanujan Journal, Volume 64, pages 1–17, (2024) 2112.15349 [math.NT] 10.1007/s11139-023-00788-0
  12. Explicit linear dependence congruence relations for the partition function modulo 4 Research in Number Theory 11, 39 (2025) 2412.17459 [math.NT] 10.1007/s40993-025-00618-w
  13. Symmetry results for multiple \(t\)-values M. E. Hoffman Math. Z. 309 (2025), no. 4, Paper No. 75. 2204.14183 [math.NT] 10.1007/s00209-024-03544-2
  14. On motivic multiple \(t\) values, Saha's basis conjecture, and generators of alternating MZV's Math. Ann. 392, 1995–2079 (2025). 2112.14613 [math.NT] 10.1007/s00208-024-02928-3
  15. On the evaluations of multiple \(S\) and \(T\) values of the form \(S(\overset{\smash{{}_{(-)}}}{2}, 1, \ldots, 1, \overset{\smash{{}_{(-)}}}{1})\) and \(T(\overset{\smash{{}_{(-)}}}{2}, 1, \ldots, 1, \overset{\smash{{}_{(-)}}}{1})\): Answers to questions of Xu, Yan, and Zhao Indagationes Mathematicae (2025) 2403.04727 [math.NT] 10.1016/j.indag.2024.12.001
  16. On the parity of coefficients of eta powers L. Mauth, and A. Medvedovsky Res. Math. Sci. 12, no. 3, Paper No. 56, pp. 40, 2025. 2411.17638 [math.NT] 10.1007/s40687-025-00507-9
  17. Aomoto and Grassmannian polylogarithms via iterated integrals H. Gangl and D. Radchenko To appear in Journal of the European Mathematical Society Part 1 of 1909.13869 [math.NT] 10.4171/JEMS/1701
  18. The Hopf algebra of formal multiple polylogarithms A. Matveiakin, D. Radchenko and D. Rudenko Int. Math. Res. Not. IMRN 2026, no. 2, Paper No. rnaf361. 2411.15071 [math.NT] 10.1093/imrn/rnaf361
  19. On a proof of Xu's Conjecture and depths of Galois descents Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 120 (2026), no. 2, Paper No. 34. 2508.02648 [math.NT] 10.1007/s13398-025-01796-z
  20. Explicit formulas for Grassmannian polylogarithms in weights 4 and 5 H. Gangl and D. Radchenko J. Number Theory 280 (2026), 537–582. Part 2 of 1909.13869 [math.NT] 10.1016/j.jnt.2025.08.011
  21. Truncated multiple zeta values M. E. Hoffman Proceedings of the 17th MSJ-SI conference on Modular forms and Multiple Zeta values 2607.04960 [math.NT] TBC

Thesis

The final version of my thesis is available in the Durham e-Theses repository. Alternatively a version of my thesis is hosted here (this version has the correct page numbering, and PDF bookmarks).

You can also view mathematica worksheets containing various supporting calculations.