The true order of the riemann zeta--function

Details The true order of the riemann zeta--function The true order of the riemann zeta--function

1998-09-17

arxiv.org/abs/math/9809090v1

Mathematics

Number Theory

89 pages

Scientific paper

For the Riemann zeta-function on the critical line the terminal estimate have been proved, which had been conjectured by Lindel\"of at the beginning of this Centure. The proof is based on the authors relations which connect the bilinear forms of the eigenvalues of the Hecke operators with sums of the Kloosterman sums. By the way, it is proved that for the Hecke series (which are associated with the eigenfunctions of the automorphic Laplacian) the natural analogue of the Lindel\"of conjecture is true also. \noindent Bibl. 14.

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