On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle

被引：0

作者：

Petrushov, O. A. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Math Notes, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2018年 / 103卷 / 5-6期

关键词：

power series; completely multiplicative function; Dirichlet series; Omega-estimates; Laplace transform;

D O I：

10.1134/S0001434618050127

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Power series whose coefficients are values of completely multiplicative functions from a general class determined by a small number of constraints are studied. The paper contains proofs of asymptotic estimates as such a power series tends to the roots of 1 along the radii of the unit circle, whence, in particular, it follows that these series cannot be extended beyond the unit disk.

引用

页码：797 / 810

页数：14

共 14 条

[1] Bari H.K., 1961, TRIGONOMETRIC SERIES
[2] Borwein P., P AM MATH SOC, V137, P1303
[3] Hardy G., 1915, The General Theory of Dirichlet's Series
[4] Hardy G. H, 1916, ACTA MATH, V41, P119
[5] Karatsuba A. A., 1983, FDN ANAL NUMBER THEO
[6] Katai I., 1967, ACTA ARITH, V13, P107, DOI 10.4064/aa-13-1-107-122
[7] Knapp A., 1992, ELLIPTIC CURVES
[8] Knapp A. W., 1992, ELLIPTIC CURVES
[9] Asymptotic Expansion of Certain Power Series with Multiplicative Coefficients near the Unit Circle
Petrushov, O. A.
[J]. MATHEMATICAL NOTES, 2017, 101 (1-2) : 297 - 309
[10] Asymptotic estimates of functions based on the behavior of their Laplace transforms near singular points
Petrushov, O. A.
[J]. MATHEMATICAL NOTES, 2013, 93 (5-6) : 906 - 916

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