Christina Giannitsi

collaborators

3 papers

math.CA2024

Averages with the Gaussian divisor: Weighted Inequalities and the Pointwise Ergodic Theorem

Christina Giannitsi, Nazar Miheisi, Hamed Mousavi

We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function $d (n)$ , that is, for a measure preserving $Z [i]$ action $T$ , the limit $$\lim_{N\rightarrow \inft…

math.NT2023

Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

Christina Giannitsi, Ben Krause, Michael Lacey +2

We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $ω \subset T$ . There is an integer $N_{ω}$ , so that every odd integer $n$ …

math.CA2023

Lower Estimate on Square Function of an Indicator Set

Christina Giannitsi, Michael T. Lacey

Let $S f$ be a discrete martingale square function. Then, for any set $V$ of positive probability, we have $E S (1_{V})^{2} \geq η P (V)$ for an absolute constan…