Xi Cen

activity

20232026

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math.NT2026

A New Bound for the Gauss Circle Problem

Xi Cen, Xitao Gao, Cheng Zhang +1

Let $E (X) = # {(a, b) \in Z^{2} : a^{2} + b^{2} \leq X} - π X$ . We prove that $E (X) = O_{ε} (X^{209/670 + ε})$ for every $ε > 0$ , uniformly for real $X \geq 4$ . This breaks the $5…

math.AP2026

A sharp regularity threshold for Schrödinger maximal estimates on standard tori

Xi Cen, Xitao Gao, Junyong Zhang

We disprove almost everywhere convergence of the Schrödinger evolution on the standard torus $\mathbb{T}^d$ for initial data $f\in H^s(\mathbb{T}^d)$ when $s<d/(d+2)$, in all…