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.

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

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

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

4. A note on the dimension of the largest Hecke submodule (with Corentin Perret-Gentil and Sandro Bettin) arXiv

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

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

7. 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

8. 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

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

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

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

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

13. 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

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

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

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

17. 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

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 A note on the Liouville function in short intervals (with Kaisa Matomaki), *Not for publication*, (2015) arXiv

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

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

21. 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

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

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

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

25. 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

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

27. 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

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

29. 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

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

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

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

33. A converse to Halasz's theorem arXiv

34. A structure theorem in probabilistic number theory arXiv

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

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

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

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