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

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

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

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

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

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

  7. (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

    8. Publications

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

  9. (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

  10. (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

  11. (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

  12. (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

  13. (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

  14. (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

  15. (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

  16. (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

  17. (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

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

  19. (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

  20. (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

  21. (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

  22. (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

  23. (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

  24. (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

  25. (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

  26. (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

  27. (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

  28. (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

  29. (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

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

  31. (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

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

  33. (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

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

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

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

  37. (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

  38. (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

  39. (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

  40. (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

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

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

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

  44. (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

  45. (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)

  46. (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

  47. (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

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

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

  50. (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