Danylo Radchenko

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.

Publications

(with K. Fedosova and K. Klinger-Logan) Convolution identities for divisor sums and modular forms
Preprint, 2023. arXiv:2312.00722
(with J. P. G. Ramos) Sharp Gaussian decay for the one-dimensional harmonic oscillator
Preprint, 2023. arXiv:2305.18546
(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
(with D. Berghaus and H. Monien) A database of modular forms on noncongruence subgroups
Preprint, 2023. arXiv:2301.02135
(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
(with S. Charlton, H. Gangl, and D. Rudenko) On the Goncharov Depth Conjecture and polylogarithms of depth two
Preprint, 2022. arXiv:2210.11938
(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
(with D. Berghaus and H. Monien) On the computation of modular forms on noncongruence subgroups
Preprint, 2022. arXiv:2207.13365
(with A. Arman, A. Bondarenko, and A. Prymak) Upper bounds on chromatic number of 𝔼ⁿ in low dimensions
Preprint, 2021. arXiv:2112.13438
(with D. Berghaus, B. Georgiev, and H. Monien) On Dirichlet eigenvalues of regular polygons
Preprint, 2021. arXiv:2103.01057
(with S. Charlton and H. Gangl) Explicit formulas for Grassmannian polylogarithms
Preprint, 2019. arXiv:1909.13869
(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
(with D. Zagier) Arithmetic properties of the Herglotz function
Journal für die reine und angewandte Mathematik 2023 no. 797, pp. 229-253 (2023), https://doi.org/10.1515/crelle-2023-0009
arXiv:2012.15805
(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
(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
arXiv:2005.02996
(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
(with D. Grigoriev) On a tropical version of the Jacobian conjecture
J. Symb. Comput. 109, pp. 399-403 (2022)
arXiv:1902.07733
(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
(with F. Villegas) Independence polynomials and hypergeometric series
Bull. Lond. Math. Soc. 53(2), pp. 1834-1848 (2021)
arXiv:1908.11231
(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
(with A. Bakan, H. Hedenmalm, A. Montes-Rodriguez, and M. Viazovska) Fourier uniqueness in even dimensions
PNAS 118(15), e2023227118 (2021)
arXiv:2007.03981
Unit distance graphs and algebraic integers
Discrete Comput. Geom. 66, pp. 269-272 (2021)
arXiv:1807.03726
(with M. Viazovska) Fourier interpolation on the real line
Publ. Math. Inst. Hautes Études Sci. 129, pp. 51-81 (2019)
arXiv:1701.00265
(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
(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
(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
(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
Higher cross-ratios and geometric functional equations for polylogarithms
PhD Thesis, Bonn University, 2016. Link
(with A.V. Bondarenko and M.S. Viazovska) Well-separated spherical designs
Constructive Approximation, Vol. 41(1), pp. 93-112 (2015)
arXiv:1303.5991
Local Maxima of the Potential Energy on Spheres
Ukr. Math. Journal, Vol. 65(10), pp. 1585-1587 (2014)
arXiv:1103.2552
(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
(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)
(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
(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
Approximation by Maps with Nonnegative Jacobian
Mat. Zametki 93:2, pp. 263-275 (2013)
arXiv:1010.5448
(with D. Leviatan and I.A. Shevchuk) Positive results and counterexamples in comonotone approximation
Constructive Approximation, Vol. 36(2), pp. 243-266 (2012)
(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