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- W3211374676 abstract "The paper continues the authors β research on the evaluation of trigonometric sums of an algebraic grid with weights. The case of an arbitrary weight function of infinite order is considered. For the parameter π of the trigonometric sum ππ(π‘),πβ(π), three cases are highlighted. If π belongs to the algebraic lattice Ξ(π‘Β·π(π)), then for any natural π the asymptotic formula is valid ππ(π‘),πβ(π‘(π, . . . ,π)) = 1 + π ( lnπ β1 det Ξ(π‘) (detΞ(π‘))π+1). If π does not belong to the algebraic lattice Ξ(π‘Β·π(π)), then two vectors are defined πΞ(π) =(π1, . . . , ππ ) and πΞ(π) from the conditions πΞ(π) β Ξ, π = πΞ( π)+ πΎπ(π) and the productπ(ππ(π)) = π1 Β· . . . Β· ππ is minimal. Asymptotic estimation is proved|ππ(π‘),πβ(π)| 6 π΅(π,β)(1 β πΏ(πΞ(π))(π(πΞ(π)))π+1 + π(π(πΞ(π))π+1 lnπ β1 det Ξ(π‘)(det Ξ(π‘))π+1))." @default.
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- W3211374676 date "2021-01-01" @default.
- W3211374676 modified "2023-09-25" @default.
- W3211374676 title "Trigonometric sums of grids of algebraic lattices with infidiff tiable weights" @default.
- W3211374676 doi "https://doi.org/10.22405/2226-8383-2021-22-3-166-178" @default.
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