Professor of Mathematics
Department of Mathematics
Caltech, 358 Linde Hall (Building #37)
1200 E California Blvd

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.

1. H. A. Helfgott, M. Radziwill, Expansion, divisibility and parity, submitted, 2021
2. K. Matomaki, M. Radziwill, T. Tao, J. Teravainen, T. Ziegler, Higher uniformity of bounded multiplicative functions in short intervals on average, submitted, 2020
3. K. Matomaki, M. Radziwill, Multiplicative functions in short intervals II, submitted, 2020
4. L-P. Arguin, P. Bourgade, M. Radziwill, The Fyodorov-Hiary-Keating Conjecture. I, submitted, 2020
5. 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
6. A. Kanigowski, M. Lemanczyk and M. Radziwill, Prime number theorem for analytic skew products, submitted, 2020
7. S. Drappeau, K. Pratt and M. Radziwill, One-level density estimates for Dirichlet L-functions with extended support, submitted, 2020
8. P. Humphries and M. Radziwill, Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics, submitted, 2019
9. A. Kanigowski, M. Lemanczyk and M. Radziwill, Rigidity in dynamics and Mobius disjointness, Fund. Math., to appear, 2019
10. S. Lester and M. Radziwill, Signs of Fourier coefficients of half-integral weight modular forms, Math. Ann., to appear, 2019
11. 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
12. L-P. Arguin, F. Ouimet and M. Radziwill, Moments of the Riemann zeta function on short intervals of the critical line, submitted, 2019
13. 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
14. E. Fouvry and M. Radziwill, Another application of Linnik's dispersion method, Chebyschevskii Sbornik 67 (3), pp. 148--164, 2018
15. E. Fouvry and M. Radziwill, Level of distribution of unbalanced convolutions, Ann. Sci. Ec. Norm. Super., to appear, 2018
16. 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
17. C. Aistleitner, V. Blomer and M. Radziwill, Triple correlation and long gaps in the spectrum of flat tori, submitted, 2018
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
26. 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
27. K. Matomaki, M. Radziwill and T. Tao, Sign patterns of the Liouville and Mobius functions, Forum Math. Sigma 4, pp. e14, 44, 2016
28. 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
29. K. Matomaki, M. Radziwill and T. Tao, An averaged form of Chowla's conjecture, Algebra Number Theory 9 (9), pp. 2167--2196, 2015
30. K. Matomaki and M. Radziwill, A note on the Liouville function in short intervals, Not for publication, 2015
31. K. Matomaki and M. Radziwill, Multiplicative functions in short intervals, Ann. of Math. (2) 183 (3), pp. 1015--1056, 2016
32. 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
33. 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
34. M. Lewko and M. Radziwill, Refinements of Gal's theorem and applications, Adv. Math. 305, pp. 280--297, 2017
35. E. K. Gnang, M. Radziwill and C. Sanna, Counting arithmetic formulas, European J. Combin. 47, pp. 40--53, 2015
36. K. Matomaki and M. Radziwill, Sign changes of Hecke eigenvalues, Geom. Funct. Anal. 25 (6), pp. 1937--1955, 2015
37. 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
38. 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
39. 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
40. M. Radziwill, Gaps between zeros of $\zeta(s)$ and the distribution of zeros of $\zeta'(s)$, Adv. Math. 257, pp. 6--24, 2014
41. 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
42. X. Li and M. Radziwill, The Riemann zeta function on vertical arithmetic progressions, Int. Math. Res. Not. (2), pp. 325--354, 2015
43. M. Radziwill, Limitations to mollifying $\zeta(s)$, 2012
44. M. Radziwill and K. Soundararajan, Continuous lower bounds for moments of zeta and L-functions, Mathematika 59 (1), pp. 119--128, 2013
45. M. Radziwill, A converse to Halasz's theorem, 2011
46. M. Radziwill, A structure theorem in probabilistic number theory, 2011
47. M. Radziwill, Large deviations in Selberg's central limit theorem, 2011
48. M. Radziwill, The 4.36th moment of the Riemann zeta-function, Int. Math. Res. Not. (18), pp. 4245-4259, 2012
49. M. Radziwill, On large deviations of additive functions, B. Sc Thesis, 2009

### Software

An implementation of the Riemann-Siegel formula on the GPU.
Code for computing quickly the eigenvalues and eigenvectors of the large sieve matrix that I investigated with Florin Boca

My public key