2003/10/08 by Yoichi Motohashi, Motohashi, Yoichi
Mathematics · #11F66 #11M99 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F66 #msc:11M99
paper · pdf · doi:10.48550/arxiv.math/0310105
19 Pages
arxiv created 2003/10/08 · openalex publication_date 2003/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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of a corrected version of the formula was later supplied by the present author in 1991, which has, however, remained unpublished for more than a decade, except for a limited distribution.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.