Discrepancy of Weyl Sequences (na) Perturbed by Rationally Periodic Functions

被引：0

作者：

Lertchoosakul, Poj ^{[1
]}

Meleshko, Sergey ^{[1
]}

机构：

[1] Suranaree Univ Technol, Inst Sci, Sch Math, 111 Univ Ave, A Muang 30000, Nakhon Ratchasi, Thailand

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2023年 / 49卷 / 04期

关键词：

Weyl sequence; Discrepancy; Low-discrepancy sequence; Uniform distribution modulo 1; Periodic perturbation;

D O I：

10.1007/s41980-023-00788-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the quantitative measure of uniform distribution of Weyl sequences perturbed by rationally periodic functions, such as (na + cos(3np/4))(n=0)(8 )where a is an irrational number. We demonstrate that the discrepancy of these sequences attains the same order of magnitude bounds for the discrepancy of classical Weyl sequences (na)(n=0)(8).

引用

页数：11

共 12 条

[1]

[Anonymous], 1910, Bull. Int. Acad. Polon. Sci. (Carcovie) A

[2]

Behnke H., 1924, ABH MATH PHYS KGL, V3, P261, DOI 10.1007/BF02954628

[3]

Blazeková O, 2011, XXIX INTERNATIONAL COLLOQUIUM ON THE MANAGEMENT OF EDUCATIONAL PROCESS, PT 1, P93

[4]

Bohl P., 1909, J MATH, V135, P189, DOI [10.1515/crll.1909.135.189, DOI 10.1515/CRLL.1909.135.189]

[5]

Hecke E., 1922, Abh. Math. Semin. Univ. Hambg, V1, P54, DOI DOI 10.1007/BF02940580

[6]

Hlawka E., 1961, ANN MAT PUR APPL, V54, P325, DOI DOI 10.1007/BF02415361

[7]

Koksma JF, 1942, Math B, V11, P7

[8]

Niederreiter H., 1973, DIOPHANTINE APPROXIM, P129

[9]

Ostrowski A., 1922, Abh. Math. Semin. Univ. Hamb., P77, DOI [10.1007/BF02940581, DOI 10.1007/BF02940581]

[10] Continued fractions with bounded partial quotients [J].

Stambul, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (04) :981-985

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