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. Explicit formulas for Grassmannian polylogarithms (Split into two papers during submission) H. Gangl and D. Radchenko 1909.13869 [math.NT]
  3. Appendix A in Complete families of embedded high genus CMC surfaces in the 3-sphere (Superseded by 2411.15071 [math.DG]) L. Heller, S. Heller and M. Traizet 2108.10214 [math.DG]
  4. 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]
  5. Creative telescoping and generating functions of (variants of) multiple zeta values K. C. Au 2404.16199 [math.NT]
  6. Symmetries of weight 6 multiple polylogarithms and Goncharov's Depth Conjecture 2405.13853 [math.NT]
  7. Minimal surfaces and alternating multiple zetas L. Heller, S. Heller and M. Traizet 2411.15071 [math.DG]
  8. The Hopf algebra of multiple polylogarithms A. Matveiakin, D. Radchenko and D. Rudenko 2411.15071 [math.NT]
  9. Euler-Kronecker constants of modular forms: beyond Dirichlet \(L\)-series A. Medvedovsky and P. Moree 2412.01803 [math.NT]
  10. Multiple polylogarithms and the Steinberg module D. Radchenko and D. Rudenko 2505.02202 [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. 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
  5. 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
  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. 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
  8. 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
  9. 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
  10. 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
  11. 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
  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 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
  15. 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
  16. On the parity of coefficients of eta powers L. Mauth, and A. Medvedovsky To appear in Research in the Mathematical Sciences 2411.17638 [math.NT] 10.1007/s40687-025-00507-9

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.