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.
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