On some conjectures and results for the Riemann zeta-function and Hecke series

Details On some conjectures and results for the Riemann zeta-function and Hecke series On some conjectures and results for the Riemann zeta-function and Hecke series

2003-11-18

arxiv.org/abs/math/0311302v1

Acta Arithmetica 99(2001), 115-145

Mathematics

Number Theory

Scientific paper

Some results and conjectures on $Z_2(s) = \int_1^\infty
|\zeta(1/2+ix)|^4x^{-s}dx (\Re s > 1)$ are presented. Consequences of these
conjectures regarding the eighth moment of $|\zeta(1/2+it)$ and the error term
in the fourth moment of $|\zeta(1/2+it)$ are discussed.

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