Maksym Radziwill

I am interested in analytic number theory and its interactions with probability theory, spectral theory and harmonic analysis.

Papers

Please note that the published version of the papers below is always the definitive one.

52. A. Dunn, M. Radziwill, Bias in cubic Gauss sums: Patterson's conjecture, submitted, 2021
51. V. Blomer, M. Radziwill, Small gaps in the spectrum of tori: asymptotic formulae, submitted, 2021
50. K. Matomaki, M. Radziwill, X. Shao, T. Tao, J. Teravainen, Singmaster's conjecture in the interior of Pascal's triangle, submitted, 2021
49. H. A. Helfgott, M. Radziwill, Expansion, divisibility and parity, submitted, 2021
48. K. Matomaki, M. Radziwill, T. Tao, J. Teravainen, T. Ziegler, Higher uniformity of bounded multiplicative functions in short intervals on average, submitted, 2020
47. K. Matomaki, M. Radziwill, Multiplicative functions in short intervals II, submitted, 2020
46. L-P. Arguin, P. Bourgade, M. Radziwill, The Fyodorov-Hiary-Keating Conjecture. I, submitted, 2020
45. O. Gorodetsky, K. Matomaki, M. Radziwill, B. Rodgers, On the variance of squarefree integers in short intervals and arithmetic progressions, Geom. Funct. Anal., to appear, 2020
44. A. Kanigowski, M. Lemanczyk and M. Radziwill, Prime number theorem for analytic skew products, submitted, 2020
43. S. Drappeau, K. Pratt and M. Radziwill, One-level density estimates for Dirichlet L-functions with extended support, submitted, 2020
42. P. Humphries and M. Radziwill, Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics, Comm. Pure Appl. Math, to appear, 2021
41. A. Kanigowski, M. Lemanczyk and M. Radziwill, Rigidity in dynamics and Mobius disjointness, Fund. Math., to appear, 2019
40. S. Lester and M. Radziwill, Signs of Fourier coefficients of half-integral weight modular forms, Math. Ann., to appear, 2019
39. W. Heap, M. Radziwill and K. Soundararajan, Sharp upper bounds for fractional moments of the Riemann zeta function, Q. J. Math. 70 (4), pp. 1387--1396, 2019
38. L-P. Arguin, F. Ouimet and M. Radziwill, Moments of the Riemann zeta function on short intervals of the critical line, Ann. Prob., to appear, 2021
37. K. Matomaki, M. Radziwill, and T. Tao, Fourier uniformity of bounded multiplicative functions in short intervals on average, Invent. Math. 220 (1), pp. 1--58, 2020
36. E. Fouvry and M. Radziwill, Another application of Linnik's dispersion method, Chebyschevskii Sbornik 67 (3), pp. 148--164, 2018
35. E. Fouvry and M. Radziwill, Level of distribution of unbalanced convolutions, Ann. Sci. Ec. Norm. Super., to appear, 2018
34. S. Bettin, C. Perret-Gentil, and M. Radziwill, A note on the dimension of the largest Hecke submodule, Int. Math. Res. Not., to appear, 2018
33. C. Aistleitner, V. Blomer and M. Radziwill, Triple correlation and long gaps in the spectrum of flat tori, submitted, 2018
32. K. Matomaki, M. Radziwill and T. Tao, Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges, Math. Annalen 374 (1-2), pp. 793--840, 2019
31. K. Matomaki, M. Radziwill and T. Tao, Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges, Proc. London Math. Soc. 118 (2), pp. 284-350, 2018
30. L-P. Arguin, D. Belius, P. Bourgade, M. Radziwill and K. Soundararajan, Maximum of the Riemann zeta function on a short interval of the critical line, Comm. Pure Appl. Math. 72 (3), pp. 500-535, 2019
29. Y. Lamzouri, S. Lester and M. Radziwill, An effective universality theorem for the Riemann zeta-function, Comm. Math. Helvetici 93 (4), pp. 709--736, 2018
28. F. Boca and M. Radziwill, Limiting distribution of eigenvalues in the large sieve matrix, J. Eur. Math. Soc. (JEMS) 22 (7), pp. 2287--2329, 2020
27. S. Bettin and H. Bui and X. Li and M. Radziwill, A quadratic divisor problem and moments of the {R}iemann zeta-function, J. Eur. Math. Soc. (JEMS) 22 (12), pp. 3953--3980, 2020
26. S. Lester and M. Radziwill, Quantum Unique Ergodicity for half-integral weight forms, Duke Math. J. 169 (2), pp. 279--351, 2020
25. V. Blomer, J. Bourgain, M. Radziwill and Z. Rudnick, Small gaps in the spectrum of the rectangular billiard, Ann. Sci. Ec. Norm. Super. (4) 50 (5), pp. 1283--1300, 2017
24. M. Radziwill and K. Soundararajan, Selberg's central limit theorem for \log |\zeta(1/2+it)|, Enseign. Math. 63 (1-2), pp. 1--19, 2017
23. K. Matomaki, M. Radziwill and T. Tao, Sign patterns of the Liouville and Mobius functions, Forum Math. Sigma 4, pp. e14, 44, 2016
22. A. J. Harper, A. Nikeghbali and M. Radziwill, A note on Helson's conjecture on moments of random multiplicative functions, Analytic number theory, pp. 145--169, Springer, Cham, 2015
21. K. Matomaki, M. Radziwill and T. Tao, An averaged form of Chowla's conjecture, Algebra Number Theory 9 (9), pp. 2167--2196, 2015
20. K. Matomaki and M. Radziwill, A note on the Liouville function in short intervals, Not for publication, 2015
19. K. Matomaki and M. Radziwill, Multiplicative functions in short intervals, Ann. of Math. (2) 183 (3), pp. 1015--1056, 2016
18. S. Lester, K. Matomaki and M. Radziwill, Small scale distribution of zeros and mass of modular forms, J. Eur. Math. Soc. (JEMS) 20 (7), pp. 1595--1627, 2018
17. S. Bettin, V. Chandee and M. Radziwill, The mean square of the product of the Riemann zeta-function with Dirichlet polynomials, J. Reine Angew. Math. 729, pp. 51--79, 2017
16. M. Lewko and M. Radziwill, Refinements of Gal's theorem and applications, Adv. Math. 305, pp. 280--297, 2017
15. E. K. Gnang, M. Radziwill and C. Sanna, Counting arithmetic formulas, European J. Combin. 47, pp. 40--53, 2015
14. K. Matomaki and M. Radziwill, Sign changes of Hecke eigenvalues, Geom. Funct. Anal. 25 (6), pp. 1937--1955, 2015
13. M. Radziwill and K. Soundararajan, Moments and distribution of central L-values of quadratic twists of elliptic curves, Invent. Math. 202 (3), pp. 1029--1068, 2015
12. Y. Lamzouri, S. Lester and M. Radziwill, Discrepancy bounds for the distribution of the Riemann zeta-function and applications, J. Anal. Math. 139 (2), pp. 453--494, 2019
11. F. Luca, M. Radziwill and I. E. Shparlinsky, On the typical size and cancelations among the coefficients of some modular forms, Math. Proc. Cambridge. Phil. Soc. 166 (1), pp. 173--189, 2019
10. M. Radziwill, Gaps between zeros of $\zeta(s)$ and the distribution of zeros of $\zeta'(s)$, Adv. Math. 257, pp. 6--24, 2014
9. V. Chandee, Y. Lee, S-C. Liu and M. Radziwill, Simple zeros of primitive Dirichlet L-functions and the asymptotic large sieve, Q. J. Math. 65 (1), pp. 63--87, 2014
8. X. Li and M. Radziwill, The Riemann zeta function on vertical arithmetic progressions, Int. Math. Res. Not. (2), pp. 325--354, 2015
7. M. Radziwill, Limitations to mollifying $\zeta(s)$, 2012
6. M. Radziwill and K. Soundararajan, Continuous lower bounds for moments of zeta and L-functions, Mathematika 59 (1), pp. 119--128, 2013
5. M. Radziwill, A converse to Halasz's theorem, 2011
4. M. Radziwill, A structure theorem in probabilistic number theory, 2011
3. M. Radziwill, Large deviations in Selberg's central limit theorem, 2011
2. M. Radziwill, The 4.36th moment of the Riemann zeta-function, Int. Math. Res. Not. (18), pp. 4245-4259, 2012
1. M. Radziwill, On large deviations of additive functions, B. Sc Thesis, 2009

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