Maksym Radziwill

Department of Mathematics
McGill University
805 Sherbrooke Street West
Montreal, Quebec H3A 0G4

Since August 2016 I'm an Assistant Professor at McGill University.
I am interested in analytic number theory and its interactions with probability theory, spectral theory and harmonic analysis.



Analytic number theory


Please note that the published version of the papers below is always the definitive one. The arxiv version is also always at least as up to date as the local copies below.

1. Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges (with Kaisa Matomaki and Terence Tao) arXiv

2. Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges (with Kaisa Matomaki and Terence Tao) arXiv

3. Maximum of the Riemann zeta function on a short interval of the critical line (with Louis-Pierre Arguin, David Belius, Paul Bourgade and Kannan Soundararajan), Comm. Pure Appl. Math., (to appear) arXiv

4. An effective universality theorem for the Riemann zeta-function (with Youness Lamzouri and Stephen Lester), Comm. Math. Helvetici, (to appear) arXiv

5. Limiting distribution of eigenvalues in the large sieve matrix (with Florin Boca) arXiv

6. A quadratic divisor problem and moments of the Riemann zeta-function (with Sandro Bettin, H. M. Bui, Xiannan Li) arXiv

7. Quantum Unique Ergodicity for half-integral weight forms (with Stephen Lester) arXiv

8. Small gaps in the spectrum of the rectangular billiard (with Valentin Blomer, Jean Bourgain and Zeev Rudnick), Annales scientifiques de l'Ecole Normale Superieure, (to appear) arXiv

9. Selberg's central limit theorem for $log |zeta(tfrac 12+it)|$ (with Kannan Soundararajan), Enseignement Mathematiques, (to appear) arXiv

10. Sign patterns of the Liouville and Mobius functions (with Kaisa Matomaki and Terence Tao), Forum of Mathematics, Sigma, 4, (2016) arXiv

11. An averaged form of Chowla's conjecture (with Kaisa Matomaki and Terence Tao), Algebra Number Theory, 9, (2015), 9, pp. 2167--2196 arXiv

12. A note on Helson's conjecture on moments of random multiplicative functions (with Adam J. Harper and Ashkan Nikeghbali), Analytic number theory, pp. 145--169 arXiv

13. A note on the Liouville function in short intervals (with Kaisa Matomaki), Not for publication, (2015) arXiv

14. Multiplicative functions in short intervals (with Kaisa Matomaki), Ann. of Math. (2), 183, (2016), 3, pp. 1015--1056 arXiv

15. Small scale distribution of zeros and mass of modular forms (with Stephen Lester and Kaisa Matomaki), J. Eur. Math. Soc., (to appear) arXiv

16. The mean square of the product of $zeta(s)$ with Dirichlet polynomials (with Sandro Bettin and Vorrapan Chandee), J. Reine Angew. Math, (to appear) arXiv

17. Refinements of G'al's theorem and applications (with Mark Lewko), Adv. Math., (to appear) arXiv

18. Counting arithmetic formulas (with Edinah K. Gnang and Carlo Sanna), European J. Combin., 47, (2015), pp. 40--53 arXiv

19. Sign changes of Hecke eigenvalues (with Kaisa Matomaki), Geom. Funct. Anal., 25, (2015), 6, pp. 1937--1955 arXiv

20. Moments and distribution of central L-values of quadratic twists of elliptic curves (with Kannan Soundararajan), Invent. Math., 202, (2015), 3, pp. 1029--1068 arXiv

21. Discrepancy bounds for the distribution of the Riemann zeta-function and applications (with Youness Lamzouri and Stephen Lester), J. Anal. Math., (to appear) arXiv

22. On the typical size and cancelations among the coefficients of some modular forms (with Florian Luca and Igor E. Shparlinsky), Math. Proc. Cambridge. Phil. Soc., (to appear) arXiv

23. Gaps between zeros of $zeta(s)$ and the distribution of zeros of $zeta'(s)$, Adv. Math., 257, (2014), pp. 6--24 arXiv

24. Simple zeros of primitive Dirichlet L-functions and the asymptotic large sieve (with Vorrapan Chandee, Yoonbok Lee and Sheng-chi Liu), Q. J. Math., 65, (2014), 1, pp. 63--87 arXiv

25. The Riemann zeta function on vertical arithmetic progressions (with Xiannan Li), Int. Math. Res. Not. IMRN, (2015), 2, pp. 325--354 arXiv

26. Limitations to mollifying $zeta(s)$ arXiv

27. Continuous lower bounds for moments of zeta and L-functions (with Kannan Soundararajan), Mathematika, 59, (2013), 1, pp. 119--128 arXiv

28. A converse to Halasz's theorem arXiv

29. A structure theorem in probabilistic number theory arXiv

30. Large deviations in Selberg's central limit theorem arXiv

31. The 4.36th moment of the Riemann zeta-function, Int. Math. Res. Not. IMRN, (2012), 18, pp. 4245--4259 arXiv

32. On large deviations of additive functions, B. Sc Thesis, (2009) arXiv


Some code you might find useful:
A port to the GPU of Bober-Hiary's implementation of Hiary's algorithm for computing the Riemann zeta-function.
Code for computing quickly the eigenvalues and eigenvectors of the large sieve matrix that I investigated with Florin BocaThe Haskell code that was used to generate this web-page from a .bib file