On the method of exponent pairs. (English) Zbl 0571.10036

Kolesnik, G.

Acta Arith. 45, 115-143 (1985).

This is a refinement of the author’s earlier paper in [Topics in classical number theory, Vol. II, Colloq. Math. Soc. János Bolyai 34, 907-926 (1984; Zbl 0552.10022)]. The following important consequences of the new results are mentioned \[ \zeta (+it)\leq t^{139/858+\epsilon},\quad \Delta (R)\leq R^{139/429+\epsilon}. \]

Reviewer: A.Balog

MSC:

11L40	Estimates on character sums
11M06	\(\zeta (s)\) and \(L(s, \chi)\)
11N45	Asymptotic results on counting functions for algebraic and topological structures

Keywords:

method of exponent pairs; multidimensional exponential sums; Riemann zeta-function; error term of asymptotic formula; number of non-isomorphic Abelian groups