DECOUPLING, EXPONENTIAL SUMS AND THE RIEMANN ZETA FUNCTION

作者：Bourgain, J.^*

来源：Journal of the American Mathematical Society, 2017, 30(1): 205-224.

DOI：10.1090/jams/860

• Riemann zeta function
• exponential sums
• decoupling

We establish a new decoupling inequality for curves in the spirit of earlier work of C. Demeter and the author which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in the work of Huxley. In particular, this leads to an improved bound
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<mml:annotation encoding="application/x-tex">|\zeta (\frac {1}{2} + it)| \ll t^{13/84 + \varepsilon }</mml:annotation>
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for the zeta function on the critical line.

• 出版日期2017-1