Danylo Radchenko

Contact: danradchenko@gmail.com

I am a CNRS researcher working at Laboratoire Paul Painlevé at the University of Lille.

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


  1. (with J. P. G. Ramos) Sharp Gaussian decay for the one-dimensional harmonic oscillator
    Preprint, 2023. arXiv:2305.18546

  2. (with K. J. Böröczky and J. P. G. Ramos) A quantitative stability result for the sphere packing problem in dimensions 8 and 24
    Preprint, 2023. arXiv:2303.07908

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

  4. (with D. Berghaus, R.S. Jones, and H. Monien) Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry
    Preprint, 2022. arXiv:2210.13229

  5. (with S. Charlton, H. Gangl, and D. Rudenko) On the Goncharov Depth Conjecture and polylogarithms of depth two
    Preprint, 2022. arXiv:2210.11938

  6. (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

  7. (with D. Berghaus and H. Monien) On the computation of modular forms on noncongruence subgroups
    Preprint, 2022. arXiv:2207.13365

  8. (with A. Arman, A. Bondarenko, and A. Prymak) Upper bounds on chromatic number of 𝔼n in low dimensions
    Preprint, 2021. arXiv:2112.13438

  9. (with D. Berghaus, B. Georgiev, and H. Monien) On Dirichlet eigenvalues of regular polygons
    Preprint, 2021. arXiv:2103.01057

  10. (with S. Charlton and H. Gangl) Explicit formulas for Grassmannian polylogarithms
    Preprint, 2019. arXiv:1909.13869

  11. (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), doi:10.4310/PAMQ.2023.v19.n1.a5

  12. (with D. Zagier) Arithmetic properties of the Herglotz function
    Journal für die reine und angewandte Mathematik, 2023, https://doi.org/10.1515/crelle-2023-0009

  13. (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)

  14. (with A. Bondarenko and K. Seip) Fourier interpolation with zeros of zeta and L-functions
    Constructive Approximation, Published: 10 Nov. 2022, https://doi.org/10.1007/s00365-022-09599-w

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

  16. (with D. Grigoriev) On a tropical version of the Jacobian conjecture
    J. Symb. Comput. 109, pp. 399–403 (2022)

  17. (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), doi:10.4153/S0008439521001016

  18. (with F. Villegas) Independence polynomials and hypergeometric series
    Bull. Lond. Math. Soc. 53 (2), pp. 1834–1848 (2021)

  19. (with S. Charlton and H. Gangl) On functional equations for Nielsen polylogarithms
    Comm. N. Th. Phys. 15 (2), pp. 363–454 (2021)

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

  21. Unit distance graphs and algebraic integers
    Discrete Comput. Geom. 66, pp. 269–272 (2021)

  22. (with M. Viazovska) Fourier interpolation on the real line
    Publ. Math. Inst. Hautes Études Sci. 129, pp. 51–81 (2019)

  23. (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)

  24. (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)

  25. (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)

  26. (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)

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

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

  29. Local Maxima of the Potential Energy on Spheres
    Ukr. Math. Journal, Vol. 65(10), pp. 1585–1587 (2014)

  30. (with A.V. Bondarenko and M.S. Viazovska) Optimal asymptotic bounds for spherical designs
    Annals of Mathematics 178(2), pp. 443–452 (2013)

  31. (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)

  32. (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)

  33. (with A.V. Bondarenko and A. Prymak) On concentrators and related approximation constants
    J. Math. Anal. Appl., Vol. 402(1) pp. 234–241 (2013)

  34. Approximation by Maps with Nonnegative Jacobian
    Mat. Zametki 93:2, pp. 263–275 (2013)

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

  36. (with I. Feschenko, L. Radzivilovsky, and M. Tantsiura) Dissecting a brick into bars
    Geometriae Dedicata, Vol. 145(1), pp. 159–168 (2010)

© 2023 Danylo Radchenko