Danylo Radchenko

Contact: danradchenko@gmail.com

I am a CNRS researcher working at Laboratoire Alexander Grothendieck at IHES.

My research interests include modular forms, algebraic number theory, convex and discrete geometry, combinatorics, as well as approximation theory and Fourier analysis.

    Preprints

  1. (with C. Wheeler) Real quadratic fields and finite quantum dilogarithms I
    Preprint, 2026. arXiv:2609.21892

  2. (with F. Gonçalves and A. Ramos) The Hörmander--Bernhardsson function in higher dimensions
    Preprint, 2026. arXiv:2608.22198

  3. (with A. Arman, A. Bondarenko, and A. Prymak) On Grünbaum's problem for symmetric configurations
    Preprint, 2026. arXiv:2607.22032

  4. (with F. Gonçalves) Sharp lower bounds for sumsets in hypercubes
    Preprint, 2026. arXiv:2607.01458

  5. (with F. Fürnsinn, and W. Zudilin) An integrality phenomenon
    Preprint, 2026. arXiv:2603.25506

  6. (with D. Berghaus, A. Bondarenko, K. Seip, and Q. Sun) The basis functions of Fourier interpolation
    Preprint, 2025. arXiv:2512.18677

  7. (with A. Arman, A. Bondarenko, and A. Prymak) On asymptotic Lebesgue's universal covering problem
    Preprint, 2025. arXiv:2512.04023

  8. (with Q. Sun) Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums
    Preprint, 2025. arXiv:2510.04873

  9. (with S. Charlton and D. Rudenko) Multiple polylogarithms and the Steinberg module
    Preprint, 2025. arXiv:2505.02202

  10. (with J. P. G. Ramos) Perturbed lattice crosses and Heisenberg uniqueness pairs
    Preprint, 2024. arXiv:2410.04557

  11. (with D. Berghaus and H. Monien) A database of modular forms on noncongruence subgroups
    Preprint, 2023. arXiv:2301.02135

  12. (with K. Klinger-Logan and S.D. Miller) The D6R4 interaction as a Poincaré series, and a related shifted convolution sum
    Preprint, 2022. arXiv:2210.00047

    13. Publications

  13. (with A. Bondarenko, J. Ortega-Cerdà, and K. Seip) The Hörmander-Bernhardsson extremal function
    To appear in Acta Mathematica
    arXiv:2504.05205

  14. (with S. Charlton, A. Matveiakin, and D. Rudenko) The Hopf algebra of multiple polylogarithms
    Int. Math. Res. Not., https://doi.org/10.1093/imrn/rnaf361
    arXiv:2411.15071

  15. (with A. Arman, A. Bondarenko, and A. Prymak) Small volume bodies of constant width with tetrahedral symmetries
    Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 21 (2025), 109, 8 pages, https://doi.org/10.3842/SIGMA.2025.109
    arXiv:2406.18428
    Illustration: 3D

  16. (with S. Charlton and H. Gangl) Explicit formulas for Grassmannian polylogarithms in weights 4 and 5
    Journal of Number Theory 280, Pages 537-582 (2026)
    arXiv:1909.13869

  17. (with S. Charlton and H. Gangl) Aomoto and Grassmannian polylogarithms via iterated integrals
    Journal of the European Mathematical Society (JEMS) (2025), https://doi.org/10.4171/JEMS/1701
    arXiv:1909.13869

  18. (with S. De Bièvre and Ch. Langrenez) The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
    Ann. Henri Poincaré (2025), https://doi.org/10.1007/s00023-025-01614-7
    Preprint, 2025. arXiv:2501.12252

  19. (with A. Bondarenko, J. Ortega-Cerdà, and K. Seip) The Hörmander-Bernhardsson Extremal Function: A Preliminary Study
    In Recent Advances in Approximation and Potential Theory, Volume honoring Ed Saff, Appl. Numer. Harmon. Anal., Springer, pp. 77-88 (2025)
    arXiv:2407.00970

  20. (with A. Arman, A. Bondarenko, and A. Prymak) On a Gallai-type problem and illumination of spiky balls and cap bodies
    Mathematika Vol. 71(2), e70017 (2025)
    Preprint, 2024. arXiv:2408.01341

  21. (with A. Arman, A. Bondarenko, F. Nazarov, and A. Prymak) Small volume bodies of constant width
    Int. Math. Res. Not. 2025(4), rnaf020 (2025)
    arXiv:2405.18501
    Illustrations: 2D, 3D

  22. (with J. P. G. Ramos) Sharp Gaussian decay for the one-dimensional harmonic oscillator
    Proc. Amer. Math. Soc. 153, pp. 1985-1991 (2025)
    arXiv:2305.18546

  23. (with K. Fedosova and K. Klinger-Logan) Convolution identities for divisor sums and modular forms
    PNAS 121(44), e2322320121 (2024)
    arXiv:2312.00722

  24. (with A. Arman, A. Bondarenko, and A. Prymak) Upper bounds on chromatic number of 𝔼n in low dimensions
    The Electronic Journal of Combinatorics, Volume 31, Issue 2 (2024)
    arXiv:2112.13438

  25. (with D. Berghaus, B. Georgiev, and H. Monien) On Dirichlet eigenvalues of regular polygons
    Journal of Mathematical Analysis and Applications, Volume 538, Issue 2, 128460 (2024)
    arXiv:2103.01057

  26. (with D. Berghaus, R.S. Jones, and H. Monien) Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry
    Advances in Computational Mathematics Volume 50, article number 38 (2024)
    arXiv:2210.13229

  27. (with K. J. Böröczky and J. P. G. Ramos) A quantitative stability result for the sphere packing problem in dimensions 8 and 24
    Journal für die reine und angewandte Mathematik, vol. 2024, no. 808, pp. 241-270 (2024)
    arXiv:2303.07908

  28. (with S. Charlton, H. Gangl, and D. Rudenko) On the Goncharov Depth Conjecture and polylogarithms of depth two
    Selecta Mathematica New Series 30, article number 27 (2024)
    arXiv:2210.11938

  29. (with D. Berghaus and H. Monien) On the computation of modular forms on noncongruence subgroups
    Mathematics of Computation 93, pp. 1399-1425 (2024)
    arXiv:2207.13365

  30. (with A. Bondarenko and K. Seip) Fourier interpolation with zeros of zeta and L-functions
    Constructive Approximation, Volume 57, pp. 405-461 (2023)
    arXiv:2005.02996

  31. (with S. Charlton and H. Gangl) Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7
    Pure and Applied Mathematics Quarterly 19(1), pp. 85-93 (2023), https://doi.org/10.4310/PAMQ.2023.v19.n1.a5
    arXiv:2012.09840

  32. (with D. Zagier) Arithmetic properties of the Herglotz function
    Journal für die reine und angewandte Mathematik, vol. 2023 no. 797, pp. 229-253 (2023), https://doi.org/10.1515/crelle-2023-0009
    arXiv:2012.15805

  33. (with H. Cohn, A. Kumar, S.D. Miller, and M. Viazovska) Universal optimality of the E8 and Leech lattices and interpolation formulas
    Annals of Mathematics 196(3), pp. 983-1082 (2022)
    arXiv:1902.05438

  34. (with M. Stoller) Fourier non-uniqueness sets from totally real number fields
    Comment. Math. Helv. 97 no. 3, pp. 513-553 (2022)
    arXiv:2108.11828

  35. (with D. Grigoriev) On a tropical version of the Jacobian conjecture
    J. Symb. Comput. 109, pp. 399-403 (2022)
    arXiv:1902.07733

  36. (with A. Bondarenko and A. Prymak) Spherical coverings and X-raying convex bodies of constant width
    Canad. Math. Bull. 65(4), pp. 860-866 (2022), https://doi.org/10.4153/S0008439521001016
    arXiv:2011.06398

  37. (with F. Villegas) Independence polynomials and hypergeometric series
    Bull. Lond. Math. Soc. 53(2), pp. 1834-1848 (2021)
    arXiv:1908.11231

  38. (with S. Charlton and H. Gangl) On functional equations for Nielsen polylogarithms
    Comm. N. Th. Phys. 15(2), pp. 363-454 (2021)
    arXiv:1908.04770

  39. (with A. Bakan, H. Hedenmalm, A. Montes-Rodriguez, and M. Viazovska) Fourier uniqueness in even dimensions
    PNAS 118(15), e2023227118 (2021)
    arXiv:2007.03981

  40. Unit distance graphs and algebraic integers
    Discrete Comput. Geom. 66, pp. 269-272 (2021)
    arXiv:1807.03726

  41. (with M. Viazovska) Fourier interpolation on the real line
    Publ. Math. Inst. Hautes Études Sci. 129, pp. 51-81 (2019)
    arXiv:1701.00265

  42. (with F. Villegas) Goursat rigid local systems of rank four
    Res. Math. Sci. 5:38, in the collection: Modular Forms are Everywhere: Celebration of Don Zagier's 65th Birthday (2018)
    arXiv:1803.08379

  43. (with A. Bondarenko, A. Mellit, A. Prymak, and M. Viazovska) There is no strongly regular graph with parameters (460,153,32,60)
    In: Dick J., Kuo F., Woźniakowski H. (eds) Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer, Cham (2018)
    arXiv:1509.06286

  44. (with H. Cohn, A. Kumar, S.D. Miller, and M. Viazovska) The sphere packing problem in dimension 24
    Annals of Mathematics 185(3), pp. 1017-1033 (2017)
    arXiv:1603.06518

  45. (with A. Bondarenko and A. Prymak) Non-existence of (76, 30, 8, 14) strongly regular graph and some structural tools
    Linear Algebra Appl. 527, pp. 53-72 (2017)
    arXiv:1410.6748

  46. Higher cross-ratios and geometric functional equations for polylogarithms
    PhD Thesis, Bonn University, 2016. Link

  47. (with A.V. Bondarenko and M.S. Viazovska) Well-separated spherical designs
    Constructive Approximation, Vol. 41(1), pp. 93-112 (2015)
    arXiv:1303.5991

  48. Local Maxima of the Potential Energy on Spheres
    Ukr. Math. Journal, Vol. 65(10), pp. 1585-1587 (2014)
    arXiv:1103.2552

  49. (with A.V. Bondarenko and M.S. Viazovska) Optimal asymptotic bounds for spherical designs
    Annals of Mathematics 178(2), pp. 443-452 (2013)
    arXiv:1009.4407

  50. (with I.V. Livinskii) Representations of algebras defined by a multiplicative relation, corresponding to the Dynkin diagrams D4, E6, E7, E8
    Ukr. Math. Journal, Vol. 64(12), pp. 1865-1892 (2013)

  51. (with A.V. Bondarenko) On a family of strongly regular graphs with λ = 1
    Journal of Combinatorial Theory, Series B 103, pp. 521-531 (2013)
    arXiv:1201.0383

  52. (with A.V. Bondarenko and A. Prymak) On concentrators and related approximation constants
    J. Math. Anal. Appl., Vol. 402(1) pp. 234-241 (2013)
    arXiv:1404.2161

  53. Approximation by Maps with Nonnegative Jacobian
    Mat. Zametki 93:2, pp. 263-275 (2013)
    arXiv:1010.5448

  54. (with D. Leviatan and I.A. Shevchuk) Positive results and counterexamples in comonotone approximation
    Constructive Approximation, Vol. 36(2), pp. 243-266 (2012)

  55. (with I. Feschenko, L. Radzivilovsky, and M. Tantsiura) Dissecting a brick into bars
    Geometriae Dedicata, Vol. 145(1), pp. 159-168 (2010)
    arXiv:0809.1883

© 2026 Danylo Radchenko