Correlations of the Riemann zeta function

Abstract

AbstractAssuming the Riemann hypothesis, we investigate the shifted moments of the zeta function introduced by Chandee Q. J. Math. 62(2011), no. 3, 545–572, where and satisfy and . We shall prove This improves upon the previous best known bounds due to Chandee and Ng, Shen, and Wong [Can. J. Math. Published online 2023:1–31. DOI 10.4153/S0008414X23000548], particularly when the differences are unbounded as . The key insight is to combine work of Heap, Radziwiłł, and Soundararajan [Q. J. Math. 70 (2019), no. 4, 1387–1396] and work of the author [arXiv preprint arXiv:2301.10634 (2023)] with the work of Harper [arXiv preprint arXiv.1305.4618 (2013)] on the moments of the zeta function.