  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.
