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A Functional Equation for the Spectral Fourth Moment of Modular Hecke L-Functions

Yoichi Motohashi
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Abstract

Albeit essential corrections are required both in his claim and in his argument, N.V. Kuznetsov observed in his Bombay article (*) of 1989 a highly interesting transformation formula for spectral sums of products of four values of modular Hecke L-functions. A complete proof of a corrected version of the formula was later supplied by the present author in 1991, which has, however, remained unpublished for more than a decade, except for a limited distribution. The aim of the present paper is to reproduce this proof of the author with some sophistications, retaining the original style as much as possible. (*) He claimed a resolution of the eighth moment problem of the Riemann zeta-function. But his argument is fatally incorrect. Our paper here concerns an essential ingredient in his argument, but we claim nothing about the eighth moment itself.

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Yoichi Motohashi. 2003-10-08. A Functional Equation for the Spectral Fourth Moment of Modular Hecke L-Functions. https://arxiv.org/abs/math/0310105

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