A method for estimating the \(L_1\) norm of an exponential sum based on arithmetic properties of the spectrum (Q2783069)

In his earlier papers, the author proved an estimate for the \(L_1\)-norms of trigonometric sums. That estimate depends on the distribution of the spectrum points over dyadic blocks and is sharp for both lacunary and nonlacunary spectra. In the used terms no improvement is possible. Hence in the paper under review not only distribution of the spectrum points over dyadic blocks is studied but also the arithmetic properties of the spectrum inside each dyadic block. The new lower estimate obtained is given in terms of the ratios of the \(L_p,\) \(p\geq 2,\) and \(L_2\) norms of dyadic blocks.NEWLINENEWLINEFor the entire collection see [Zbl 0981.00017].