Maksym Radziwiłł

An averaged form of Chowla’s conjecture

Let

CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA AND L-FUNCTIONS

\lambda

A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions

denote the Liouville function. A well known conjecture of Chowla asserts that for any distinct natural numbers

Counting arithmetic formulas

h_1,\dots,h_k

Multiplicative functions in short intervals

, one has

The Riemann Zeta Function on Vertical Arithmetic Progressions

\sum_{1 \leq n \leq X} \lambda(n+h_1) \dotsm \lambda(n+h_k) = o(X)

The 4.36th Moment of the Riemann Zeta-Function

as

Moments and distribution of central L-values of quadratic twists of elliptic curves

X \to \infty

Sign changes of Hecke eigenvalues

. This conjecture remains unproven for any

Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

h_1,\dots,h_k