Skip to main content

Research Repository

Advanced Search

Outputs (16)

Large odd order character sums and improvements of the P\'olya-Vinogradov inequality (2022)
Journal Article
Lamzouri, Y., & Mangerel, A. P. (2022). Large odd order character sums and improvements of the P\'olya-Vinogradov inequality. Transactions of the American Mathematical Society, 375, 3759-3793. https://doi.org/10.1090/tran/8607

For a primitive Dirichlet character modulo q, we dene M() = maxt j P nt (n)j. In this paper, we study this quantity for characters of a xed odd order g 3. Our main result provides a further improvement of the classical Polya-Vinogradov inequality in... Read More about Large odd order character sums and improvements of the P\'olya-Vinogradov inequality.

On the orbits of multiplicative pairs (2020)
Journal Article
Klurman, O., & Mangerel, A. P. (2020). On the orbits of multiplicative pairs. Algebra & Number Theory, 14(1), 155–189. https://doi.org/10.2140/ant.2020.14.155

We characterize all pairs of completely multiplicative functions fg:N→T, where T denotes the unit circle, such that ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ {(f(n),g(n+1))}n≥1 ≠T×T. In so doing, we settle an old conjecture of Zoltán Daróczy and Imre Kátai. Read More about On the orbits of multiplicative pairs.

On the bivariate Erdős–Kac theorem and correlations of the Möbius function (2019)
Journal Article
Mangerel, A. P. (2019). On the bivariate Erdős–Kac theorem and correlations of the Möbius function. Mathematical Proceedings of the Cambridge Philosophical Society, 169(3), 547-605. https://doi.org/10.1017/s0305004119000288

Given a positive integer n let ω (n) denote the number of distinct prime factors of n, and let a be fixed positive integer. Extending work of Kubilius, we develop a bivariate probabilistic model to study the joint distribution of the deterministic ve... Read More about On the bivariate Erdős–Kac theorem and correlations of the Möbius function.

Rigidity theorems for multiplicative functions (2018)
Journal Article
Klurman, O., & Mangerel, A. P. (2018). Rigidity theorems for multiplicative functions. Mathematische Annalen, 372(1-2), 651–697. https://doi.org/10.1007/s00208-018-1724-6

We establish several results concerning the expected general phenomenon that, given a multiplicative function f:N→C , the values of f(n) and f(n+a) are “generally” independent unless f is of a “special” form. First, we classify all bounded completel... Read More about Rigidity theorems for multiplicative functions.