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Publications

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

Published papers

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

  2. (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

  3. (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

  4. (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

  5. (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

  6. (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

  7. (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

  8. (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

  9. (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

  10. (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

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

  12. (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

  13. (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

  14. (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

  15. (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

  16. (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

  17. (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

  18. (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

  19. (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

  20. (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

  21. (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

  22. (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

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

  24. (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

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

  26. (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

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

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

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

  30. (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

  31. (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

  32. (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

  33. (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

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

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

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

  37. (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

  38. (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)

  39. (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

  40. (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

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

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

  43. (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

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