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.

(with A. Arman, A. Bondarenko, F. Nazarov, and A. Prymak)

*Small volume bodies of constant width*

Preprint, 2024. arXiv:2405.18501

Illustrations: 2D, 3D(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 D. Berghaus and H. Monien)

*A database of modular forms on noncongruence subgroups*

Preprint, 2023. arXiv:2301.02135(with K. Klinger-Logan and S.D. Miller)

*The D*^{6}R^{4}interaction as a Poincaré series, and a related shifted convolution sum

Preprint, 2022. arXiv:2210.00047(with S. Charlton and H. Gangl)

*Explicit formulas for Grassmannian polylogarithms*

Preprint, 2019. arXiv:1909.13869(with A. Arman, A. Bondarenko, and A. Prymak)

*Upper bounds on chromatic number of 𝔼*^{n}in low dimensions

The Electronic Journal of Combinatorics, Volume**31**, Issue**2**(2024)

arXiv:2112.13438(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(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(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(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(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(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(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**E*_{8}and Leech lattices and interpolation formulas

Annals of Mathematics**196(3)**, pp. 983-1082 (2022)

arXiv:1902.05438(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**D*_{4},*E*_{6},*E*_{7},*E*_{8}

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

© 2024 Danylo Radchenko