Department of Mathematics

Caltech, 358 Linde Hall (Building #37)

1200 E California Blvd

Pasadena, CA, 91125

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

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

- A. Dunn, M. Radziwill, Bias in cubic Gauss sums: Patterson's conjecture, submitted, 2021
- V. Blomer, M. Radziwill, Small gaps in the spectrum of tori: asymptotic formulae, submitted, 2021
- K. Matomaki, M. Radziwill, X. Shao, T. Tao, J. Teravainen, Singmaster's conjecture in the interior of Pascal's triangle, submitted, 2021
- H. A. Helfgott, M. Radziwill, Expansion, divisibility and parity, submitted, 2021
- K. Matomaki, M. Radziwill, T. Tao, J. Teravainen, T. Ziegler, Higher uniformity of bounded multiplicative functions in short intervals on average, submitted, 2020
- K. Matomaki, M. Radziwill, Multiplicative functions in short intervals II, submitted, 2020
- L-P. Arguin, P. Bourgade, M. Radziwill, The Fyodorov-Hiary-Keating Conjecture. I, submitted, 2020
- 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 - A. Kanigowski, M. Lemanczyk and M. Radziwill, Prime number theorem for analytic skew products, submitted, 2020
- S. Drappeau, K. Pratt and M. Radziwill, One-level density estimates for Dirichlet L-functions with extended support, submitted, 2020
- 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 - A. Kanigowski, M. Lemanczyk and M. Radziwill, Rigidity in dynamics and Mobius disjointness,
*Fund. Math.*, to appear, 2019 - S. Lester and M. Radziwill, Signs of Fourier coefficients of half-integral weight modular forms,
*Math. Ann.*, to appear, 2019 - 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 - 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 - 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 - E. Fouvry and M. Radziwill, Another application of Linnik's dispersion method,
*Chebyschevskii Sbornik***67**(3), pp. 148--164, 2018 - E. Fouvry and M. Radziwill, Level of distribution of unbalanced convolutions,
*Ann. Sci. Ec. Norm. Super.*, to appear, 2018 - 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 - C. Aistleitner, V. Blomer and M. Radziwill, Triple correlation and long gaps in the spectrum of flat tori, submitted, 2018
- 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 - 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 - 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 - 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 - 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 - 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 - S. Lester and M. Radziwill, Quantum Unique Ergodicity for half-integral weight forms,
*Duke Math. J.***169**(2), pp. 279--351, 2020 - 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 - 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 - K. Matomaki, M. Radziwill and T. Tao, Sign patterns of the Liouville and Mobius functions,
*Forum Math. Sigma***4**, pp. e14, 44, 2016 - 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 - K. Matomaki, M. Radziwill and T. Tao, An averaged form of Chowla's conjecture,
*Algebra Number Theory***9**(9), pp. 2167--2196, 2015 - K. Matomaki and M. Radziwill, A note on the Liouville function in short intervals, Not for publication, 2015
- K. Matomaki and M. Radziwill, Multiplicative functions in short intervals,
*Ann. of Math. (2)***183**(3), pp. 1015--1056, 2016 - 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 - 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 - M. Lewko and M. Radziwill, Refinements of Gal's theorem and applications,
*Adv. Math.***305**, pp. 280--297, 2017 - E. K. Gnang, M. Radziwill and C. Sanna, Counting arithmetic formulas,
*European J. Combin.***47**, pp. 40--53, 2015 - K. Matomaki and M. Radziwill, Sign changes of Hecke eigenvalues,
*Geom. Funct. Anal.***25**(6), pp. 1937--1955, 2015 - 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 - 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 - 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 - M. Radziwill, Gaps between zeros of $\zeta(s)$ and the distribution of zeros of $\zeta'(s)$,
*Adv. Math.***257**, pp. 6--24, 2014 - 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 - X. Li and M. Radziwill, The Riemann zeta function on vertical arithmetic progressions,
*Int. Math. Res. Not.*(2), pp. 325--354, 2015 - M. Radziwill, Limitations to mollifying $\zeta(s)$, 2012
- M. Radziwill and K. Soundararajan, Continuous lower bounds for moments of zeta and L-functions,
*Mathematika***59**(1), pp. 119--128, 2013 - M. Radziwill, A converse to Halasz's theorem, 2011
- M. Radziwill, A structure theorem in probabilistic number theory, 2011
- M. Radziwill, Large deviations in Selberg's central limit theorem, 2011
- M. Radziwill, The 4.36th moment of the Riemann zeta-function,
*Int. Math. Res. Not.*(18), pp. 4245-4259, 2012 - M. Radziwill, On large deviations of additive functions, B. Sc Thesis, 2009

Code for computing quickly the eigenvalues and eigenvectors of the large sieve matrix that I investigated with Florin Boca