Maksym Radziwill

Professor of Mathematics
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. The arxiv version is also always at least as up to date as the local copies below.

Papers

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. Sharp upper bounds for fractional moments of the Riemann zeta function (with Winston Heap, Kannan Soundararajan) arXiv

2. Moments of the Riemann zeta function on short intervals of the critical line (with Louis-Pierre Arguin, Frederic Ouimet) arXiv

3. Fourier uniformity of bounded multiplicative functions in short intervals on average (with Kaisa Matomaki and Terence Tao) arXiv

4. Another application of Linnik's dispersion method (with Etienne Fouvry) arXiv

5. Level of distribution of unbalanced convolutions (with Etienne Fouvry) arXiv

6. A note on the dimension of the largest Hecke submodule (with Corentin Perret-Gentil and Sandro Bettin), Int. Math. Res. Not., (to appear) arXiv

7. Triple correlation and long gaps in the spectrum of flat tori (with Christoph Aistleitner and Valentin Blomer) arXiv

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

9. Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges (with Kaisa Matomaki and Terence Tao), Proc. London Math. Soc., (to appear) arXiv

10. 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

11. An effective universality theorem for the Riemann zeta-function (with Youness Lamzouri and Stephen Lester), Comment. Math. Helv., 93, (2018), 4, pp. 709--736 arXiv

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

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

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

15. Small gaps in the spectrum of the rectangular billiard (with Valentin Blomer, Jean Bourgain and Zeev Rudnick), Ann. Sci. Ec. Norm. Super. (4), 50, (2017), 5, pp. 1283--1300 arXiv

16. Selberg's central limit theorem for {$log{|zeta(1/2+it)|}$} (with Kannan Soundararajan), Enseign. Math., 63, (2017), 1-2, pp. 1--19 arXiv

17. Sign patterns of the {L}iouville and {M}"{o}bius functions (with Kaisa Matomaki and Terence Tao), Forum Math. Sigma, 4, (2016), pp. e14, 44 arXiv

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

19. 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

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

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

22. Small scale distribution of zeros and mass of modular forms (with Stephen Lester and Kaisa Matomaki), J. Eur. Math. Soc. (JEMS), 20, (2018), 7, pp. 1595--1627 arXiv

23. The mean square of the product of the {R}iemann zeta-functionnt with {D}irichlet polynomials (with Sandro Bettin and Vorrapan Chandee), J. Reine Angew. Math., 729, (2017), pp. 51--79 arXiv

24. Refinements of {G}'{a}l's theorem and applications (with Mark Lewko), Adv. Math., 305, (2017), pp. 280--297 arXiv

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

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

27. 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

28. An effective universality theorem for the Riemann zetant function (with Youness Lamzouri and Stephen Lester), J. Anal. Math., (to appear) arXiv

29. 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

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

31. 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

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

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

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

35. A converse to Halasz's theorem arXiv

36. A structure theorem in probabilistic number theory arXiv

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

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

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


Software

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 Boca
The Haskell code that was used to generate this web-page from a .bib file

Public Key

My public key