Maksym Radziwill

Professor of Mathematics

Contact:

Courant Institute of Mathematical Sciences
251 Mercer Street, New York, NY, 10012
first dot last at gmail dot com

Preprints

  1. Matomäki, Kaisa, Maksym Radziwiłł, Xuancheng Shao, Terence Tao, and Joni Teräväinen. “Higher Uniformity of Arithmetic Functions in Short Intervals II. Almost All Intervals.” Invent. Math., to appear.
  2. Pandey, Mayank, and Maksym Radziwiłł. “\(L^1\) Means of Exponential Sums with Multiplicative Coefficients. I.” Compositio. Math., to appear.
  3. Kanigowski, Adam, and Maksym Radziwiłł. “Density of Orbits of Horocycle Flows at Sub-Quadratic Polynomial Times,” 2025.
  4. Pandey, Mayank, and Maksym Radziwiłł. “\(L^1\) Means of Exponential Sums with Multiplicative Coefficients. II,” 2025.
  5. Chandee, Vorrapan, Xiannan Li, Kaisa Matomäki, and Maksym Radziwiłł. “The Sixth Moment of Dirichlet L-Functions at the Central Point,” 2024.
  6. Forni, Giovanni, Adam Kanigowski, and Maksym Radziwiłł. “Horocycle Flow at Product of Two Primes,” 2024.
  7. Technau, Niclas, and Maksym Radziwiłł. “Gap Distribution of \(\sqrt{n} \pmod{1}\) and the Circle Method,” 2024.
  8. Arguin, Louis-Pierre, Paul Bourgade, and Maksym Radziwiłł. “The Fyodorov-Hiary-Keating Conjecture. II,” 2023.
  9. Radziwiłł, Maksym, and Liyang Yang. “Non-Vanishing of Twists of \(\text{GL}_4(\mathbb{A}_{\mathbb{Q}})\) L-Functions,” 2023.
  10. Helfgott, Harald, and Maksym Radziwiłł. “Expansion, Divisibility and Parity,” 2021.
  11. Arguin, Louis-Pierre, Paul Bourgade, and Maksym Radziwiłł. “The Fyodorov-Hiary-Keating Conjecture. I,” 2020.
  12. Matomäki, Kaisa, and Maksym Radziwiłł. “Multiplicative Functions in Short Intervals II,” 2020.

Published papers

  1. Aistleitner, Christoph, Valentin Blomer, and Maksym Radziwiłł. “Triple Correlation and Long Gaps in the Spectrum of Flat Tori.” J. Eur. Math. Soc. (JEMS) 26, no. 1 (2024): 41–74. Published version.
  2. Chandee, Vorrapan, Xiannan Li, Kaisa Matomäki, and Maksym Radziwiłł. “The Eighth Moment of Dirichlet \(L\)-Functions II.” Duke Math. J. 173, no. 18 (2024): 3453–93. Published version.
  3. Dunn, Alexander, and Maksym Radziwiłł. “Bias in Cubic Gauss Sums: Patterson’s Conjecture.” Ann. Of Math. (2) 200, no. 3 (2024): 967–1057. Published version.
  4. Kanigowski, Adam, Mariusz Lemańczyk, and Maksym Radziwiłł. “Prime Number Theorem for Analytic Skew Products.” Ann. Of Math. (2) 199, no. 2 (2024): 591–705. Published version.
  5. Radziwiłł, Maksym, and Andrei Shubin. “Poissonian Pair Correlation for \(\alpha n^\theta \bmod 1\).” Int. Math. Res. Not. IMRN, no. 9 (2024): 7654–79. Published version.
  6. Radziwiłł, Maksym, and Kannan Soundararajan. “Conditional Lower Bounds on the Distribution of Central Values in Families of \(L\)-Functions.” Acta Arith. 214 (2024): 481–97. Published version.
  7. Blomer, Valentin, and Maksym Radziwiłł. “Small Gaps in the Spectrum of Tori: Asymptotic Formulae.” Comm. Math. Phys. 403, no. 1 (2023): 155–80. Published version.
  8. Drappeau, Sary, Kyle Pratt, and Maksym Radziwiłł. “One-Level Density Estimates for Dirichlet \(L\)-Functions with Extended Support.” Algebra Number Theory 17, no. 4 (2023): 805–30. Published version.
  9. Matomäki, Kaisa, Maksym Radziwiłł, Terence Tao, Joni Teräväinen, and Tamar Ziegler. “Higher Uniformity of Bounded Multiplicative Functions in Short Intervals on Average.” Ann. Of Math. (2) 197, no. 2 (2023): 739–857. Published version.
  10. Radziwiłł, Maksym. “The Distribution of Prime Numbers [Book Review of 3971232].” Bull. Amer. Math. Soc. (N.S.) 60, no. 1 (2023): 139–44.
  11. Fouvry, Étienne, and Maksym Radziwiłł. “Level of Distribution of Unbalanced Convolutions.” Ann. Sci. Éc. Norm. Supér. (4) 55, no. 2 (2022): 537–68. Published version.
  12. Humphries, Peter, and Maksym Radziwiłł. “Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics.” Comm. Pure Appl. Math. 75, no. 9 (2022): 1936–96. Published version.
  13. Matomäki, Kaisa, Maksym Radziwiłł, Xuancheng Shao, Terence Tao, and Joni Teräväinen. “Singmaster’s Conjecture in the Interior of Pascal’s Triangle.” Q. J. Math. 73, no. 3 (2022): 1137–77. Published version.
  14. Arguin, Louis-Pierre, Frédéric Ouimet, and Maksym Radziwiłł. “Moments of the Riemann Zeta Function on Short Intervals of the Critical Line.” Ann. Probab. 49, no. 6 (2021): 3106–41. Published version.
  15. Bettin, Sandro, Corentin Perret-Gentil, and Maksym Radziwiłł. “A Note on the Dimension of the Largest Simple Hecke Submodule.” Int. Math. Res. Not. IMRN, no. 7 (2021): 4907–19. Published version.
  16. Gorodetsky, Ofir, Kaisa Matomäki, Maksym Radziwiłł, and Brad Rodgers. “On the Variance of Squarefree Integers in Short Intervals and Arithmetic Progressions.” Geom. Funct. Anal. 31, no. 1 (2021): 111–49. Published version.
  17. Kanigowski, Adam, Mariusz Lemańczyk, and Maksym Radziwiłł. “Rigidity in Dynamics and Möbius Disjointness.” Fund. Math. 255, no. 3 (2021): 309–36. Published version.
  18. Lester, Stephen, and Maksym Radziwiłł. “Signs of Fourier Coefficients of Half-Integral Weight Modular Forms.” Math. Ann. 379, no. 3-4 (2021): 1553–1604. Published version.
  19. Bettin, Sandro, H. M. Bui, Xiannan Li, and Maksym Radziwiłł. “A Quadratic Divisor Problem and Moments of the Riemann Zeta-Function.” J. Eur. Math. Soc. (JEMS) 22, no. 12 (2020): 3953–80. Published version.
  20. Boca, Florin P., and Maksym Radziwiłł. “Limiting Distribution of Eigenvalues in the Large Sieve Matrix.” J. Eur. Math. Soc. (JEMS) 22, no. 7 (2020): 2287–2329. Published version.
  21. Lester, Stephen, and Maksym Radziwiłł. “Quantum Unique Ergodicity for Half-Integral Weight Automorphic Forms.” Duke Math. J. 169, no. 2 (2020): 279–351. Published version.
  22. Matomäki, Kaisa, Maksym Radziwiłł, and Terence Tao. “Fourier Uniformity of Bounded Multiplicative Functions in Short Intervals on Average.” Invent. Math. 220, no. 1 (2020): 1–58. Published version.
  23. Arguin, Louis-Pierre, David Belius, Paul Bourgade, Maksym Radziwiłł, and Kannan Soundararajan. “Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line.” Comm. Pure Appl. Math. 72, no. 3 (2019): 500–535. Published version.
  24. Heap, Winston, Maksym Radziwiłł, and K. Soundararajan. “Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function.” Q. J. Math. 70, no. 4 (2019): 1387–96. Published version.
  25. Lamzouri, Youness, Stephen Lester, and Maksym Radziwiłł. “Discrepancy Bounds for the Distribution of the Riemann Zeta-Function and Applications.” J. Anal. Math. 139, no. 2 (2019): 453–94. Published version.
  26. Luca, Florian, Maksym Radziwiłł, and Igor E. Shparlinski. “On the Typical Size and Cancellations Among the Coefficients of Some Modular Forms.” Math. Proc. Cambridge Philos. Soc. 166, no. 1 (2019): 173–89. Published version.
  27. Matomäki, Kaisa, Maksym Radziwiłł, and Terence Tao. “Correlations of the von Mangoldt and Higher Divisor Functions I. Long Shift Ranges.” Proc. Lond. Math. Soc. (3) 118, no. 2 (2019): 284–350. Published version.
  28. ———. “Correlations of the von Mangoldt and Higher Divisor Functions II: Divisor Correlations in Short Ranges.” Math. Ann. 374, no. 1-2 (2019): 793–840. Published version.
  29. Fouvry, Étienne, and Maksym Radziwiłł. “Another Application of Linnik Dispersion Method.” Chebyshevskii Sb. 19, no. 3 (2018): 148–63. Published version.
  30. Lamzouri, Youness, Stephen Lester, and Maksym Radziwill. “An Effective Universality Theorem for the Riemann Zeta Function.” Comment. Math. Helv. 93, no. 4 (2018): 709–36. Published version.
  31. Lester, Stephen, Kaisa Matomäki, and Maksym Radziwiłł. “Small Scale Distribution of Zeros and Mass of Modular Forms.” J. Eur. Math. Soc. (JEMS) 20, no. 7 (2018): 1595–1627. Published version.
  32. Matomäki, Kaisa, and Maksym Radziwiłł. “Multiplicative Functions in Short Intervals, and Correlations of Multiplicative Functions.” In Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. II. Invited Lectures, 321–43. World Sci. Publ., Hackensack, NJ, 2018.
  33. Bettin, Sandro, Vorrapan Chandee, and Maksym Radziwiłł. “The Mean Square of the Product of the Riemann Zeta-Function with Dirichlet Polynomials.” J. Reine Angew. Math. 729 (2017): 51–79. Published version.
  34. Blomer, Valentin, Jean Bourgain, Maksym Radziwiłł, and Zeév Rudnick. “Small Gaps in the Spectrum of the Rectangular Billiard.” Ann. Sci. Éc. Norm. Supér. (4) 50, no. 5 (2017): 1283–1300. Published version.
  35. Lewko, Mark, and Maksym Radziwiłł. “Refinements of Gál’s Theorem and Applications.” Adv. Math. 305 (2017): 280–97. Published version.
  36. Radziwiłł, Maksym, and Kannan Soundararajan. “Selberg’s Central Limit Theorem for \(\log{|\zeta(1/2+it)|}\).” Enseign. Math. 63, no. 1-2 (2017): 1–19. Published version.
  37. Matomäki, Kaisa, and Maksym Radziwiłł. “Multiplicative Functions in Short Intervals.” Ann. Of Math. (2) 183, no. 3 (2016): 1015–56. Published version.
  38. Matomäki, Kaisa, Maksym Radziwiłł, and Terence Tao. “Sign Patterns of the Liouville and Möbius Functions.” Forum Math. Sigma 4 (2016): Paper No. e14, 44. Published version.
  39. Gnang, Edinah K., Maksym Radziwiłł, and Carlo Sanna. “Counting Arithmetic Formulas.” European J. Combin. 47 (2015): 40–53. Published version.
  40. Harper, Adam J., Ashkan Nikeghbali, and Maksym Radziwiłł. “A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions.” In Analytic Number Theory, 145–69. Springer, Cham, 2015.
  41. Li, Xiannan, and Maksym Radziwiłł. “The Riemann Zeta Function on Vertical Arithmetic Progressions.” Int. Math. Res. Not. IMRN, no. 2 (2015): 325–54. Published version.
  42. Matomäki, Kaisa, and Maksym Radziwiłł. “Sign Changes of Hecke Eigenvalues.” Geom. Funct. Anal. 25, no. 6 (2015): 1937–55. Published version.
  43. Matomäki, Kaisa, Maksym Radziwiłł, and Terence Tao. “An Averaged Form of Chowla’s Conjecture.” Algebra Number Theory 9, no. 9 (2015): 2167–96. Published version.
  44. Radziwiłł, Maksym, and K. Soundararajan. “Moments and Distribution of Central \(L\)-Values of Quadratic Twists of Elliptic Curves.” Invent. Math. 202, no. 3 (2015): 1029–68. Published version.
  45. Chandee, Vorrapan, Yoonbok Lee, Sheng-Chi Liu, and Maksym Radziwiłł. “Simple Zeros of Primitive Dirichlet \(L\)-Functions and the Asymptotic Large Sieve.” Q. J. Math. 65, no. 1 (2014): 63–87. Published version.
  46. Radziwiłł, Maksym. “Gaps Between Zeros of \(\zeta(s)\) and the Distribution of Zeros of \(\zeta'(s)\).” Adv. Math. 257 (2014): 6–24. Published version.
  47. Radziwiłł, Maksym, and Kannan Soundararajan. “Continuous Lower Bounds for Moments of Zeta and \(L\)-Functions.” Mathematika 59, no. 1 (2013): 119–28. Published version.
  48. Radziwiłł, Maksym. “The 4.36th Moment of the Riemann Zeta-Function.” Int. Math. Res. Not. IMRN, no. 18 (2012): 4245–59. Published version.

Old preprints

  1. Matomäki, Kaisa, and Maksym Radziwiłł. “A Note on the Liouville Function in Short Intervals,” 2015.
  2. Radziwiłł, Maksym. “Limitation to Mollifying \(\zeta(s)\),” 2012.
  3. ———. “A Converse to Halasz’s Theorem,” 2011.
  4. ———. “A Structure Theorem in Probabilistic Number Theory,” 2011.
  5. ———. “Large Deviations in Selberg’s Central Limit Theorem,” 2011.
  6. ———. “On Large Deviations of Additive Functions,” 2009.