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This article is cited in 2 scientific papers (total in 2 papers)
BRIEF MESSAGE
Trigonometric sums of nets of algebraic lattices
E. M. Rarova Tula State L. N. Tolstoy Pedagogical University
(Tula)
Abstract:
The paper continues the author's research on the evaluation of trigonometric sums of an algebraic net with weights with the simplest weight function of the second order.
For the parameter →m of the trigonometric sum SM(t),→ρ1(→m), three cases are highlighted.
If →m belongs to the algebraic lattice Λ(t⋅T(→a)), then the asymptotic formula is valid
SM(t),→ρ1(t(m,…,m))=1+O(lns−1detΛ(t)(detΛ(t))2).
If →m does not belong to the algebraic lattice Λ(t⋅T(→a)), then two vectors are defined →nΛ(→m)=(n1,…,ns) and →kΛ(→m) from the conditions →kΛ(→m)∈Λ, →m=→nΛ(→M)+→Kλ(→m) and the product q(→nλ(→m))=¯n1⋅…⋅¯ns is minimal. Asymptotic estimation is proved
SM(t),→ρ1(t(m,…,m))=1−δ(→kΛ(→m))q(→nΛ(→m))2+O(q(→nΛ(→m))2lns−1detΛ(t)(detΛ(t))2).
Keywords:
algebraic lattices, algebraic net, trigonometric sums of algebraic net with weights, weight functions.
Received: 18.03.2017 Accepted: 12.07.2019
Citation:
E. M. Rarova, “Trigonometric sums of nets of algebraic lattices”, Chebyshevskii Sb., 20:2 (2019), 399–405
Linking options:
https://www.mathnet.ru/eng/cheb780 https://www.mathnet.ru/eng/cheb/v20/i2/p399
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Abstract page: | 170 | Full-text PDF : | 42 | References: | 21 |
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