On asymptotic behavior of Dirichlet inverse

被引：2

作者：

Baustian, Falko ^{[1
]}

Bobkov, Vladimir ^{[2
,3
,4
]}

机构：

[1] Univ Rostock, Dept Math, Ulmenstr 69, D-18057 Rostock, Germany

[2] Univ West Bohemia, Dept Math, Fac Appl Sci, Univ 8, Plzen 30100, Czech Republic

[3] Univ West Bohemia, NTIS, Fac Appl Sci, Univ 8, Plzen 30100, Czech Republic

[4] RAS, Inst Math, Ufa Fed Res Ctr, Chernyshevsky Str 112, Ufa 450008, Russia

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2020年 / 16卷 / 06期

关键词：

Dirichlet inverse; Dirichlet convolution; asymptotics; ordered factorizations; PRIME NUMBER THEOREM;

D O I：

10.1142/S1793042120500700

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f (n) be an arithmetic function with f (1) not equal 0 and let f(-1) (n) be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behavior of vertical bar f(-1) (n)vertical bar with regard to the asymptotic behavior of vertical bar f (n)vertical bar assuming that the latter one grows or decays with at most polynomial or exponential speed. As a by-product, we obtain simple but constructive upper bounds for the number of ordered factorizations of n into k factors.

引用

页码：1337 / 1354

页数：18

共 23 条

[1]

Apostol TM., 1998, Introduction to analytic number theory, V5th

[2] Basis properties of eigenfunctions of the p-Laplacian [J].

Binding, Paul ;

Boulton, Lyonell ;

Cepicka, Jan ;

Drabek, Pavel ;

Girg, Petr .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (12) :3487-3494

[3] On the number of ordered factorizations of natural numbers [J].

Chor, B ;

Lemke, P ;

Mador, Z .

DISCRETE MATHEMATICS, 2000, 214 (1-3) :123-133

[4] Constructive bounds on ordered factorizations [J].

Coppersmith, D ;

Lewenstein, M .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2005, 19 (02) :301-303

[5]

Haukkanen P., 2000, NOTES NUMBER THEORY, V6, p118?124

[6]

Haukkanen P., 1997, NIEUW ARCH WISKD, V15, P73

[7] A Hilbert space of Dirichlet series and systems of dilated functions in L(2)(0,1) [J].

Hedenmalm, H ;

Lindqvist, P ;

Seip, K .

DUKE MATHEMATICAL JOURNAL, 1997, 86 (01) :1-37

[8]

Hedenmalm H., 1999, DUKE MATH J, V99, P175

[9]

Hille E., 1936, ACTA ARITH, V2, P134, DOI DOI 10.4064/AA-2-1-134-144

[10]

Hwang HK, 2011, ELECTRON J PROBAB, V16, P347

← 1 2 3 →