Zeros of linear combinations of Dirichlet L-functions on the critical line

被引：0

作者：

Dousselin, Jeremy ^{[1
]}

机构：

[1] Inst Elie Cartan Lorraine, Vandoeuvre Les Nancy, France

来源：

FORUM MATHEMATICUM | 2025年 / 37卷 / 06期

关键词：

Dirichlet L-functions; critical line; mollification; linear combination of L functions; ZETA-FUNCTION;

D O I：

10.1515/forum-2023-0453

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F be a linear combination (of a certain form) of N >= 1 Dirichlet L-functions attached to even (or odd) primitive characters. Selberg proved that a positive proportion of non-trivial zeros of F lie on the critical line. Our work here is to provide an explicit lower bound for this proportion. In particular, we show that the lower bound 2.16 x 10 - 6 / ( N log N ) is admissible for large N.

引用

页码：1871 / 1912

页数：42

共 28 条

[1]

Bauer P., 1997, THESIS JW GOETHE U F

[2] Zeros of Dirichlet L-series on the critical line [J].

Bauer, PJ .

ACTA ARITHMETICA, 2000, 93 (01) :37-52

[3]

Bohr H, 1914, CR HEBD ACAD SCI, V158, P106

[4] On the distribution of zeros of linear combinations of Euler products [J].

Bombieri, E ;

Hejhal, DA .

DUKE MATHEMATICAL JOURNAL, 1995, 80 (03) :821-862

[5]

Burgess D.A., 1962, Proc. London Math. Soc, V12, P193, DOI DOI 10.1112/PLMS/S3-12.1.193

[6] Critical zeros of lacunary L-functions [J].

Conrey, J. B. ;

Iwaniec, H. .

ACTA ARITHMETICA, 2020, 195 (03) :217-268

[7] Critical zeros of Dirichlet L-functions [J].

Conrey, J. Brian ;

Iwaniec, Henryk ;

Soundararajan, Kannan .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 681 :175-198

[8]

Davenport H., 1980, Multiplicative number theory, V74

[9]

Gabriel R.M., 1927, J. Lond. Math. Soc., V2, P112

[10] The zeros of Rienmann's zeta-function on the critical line. [J].

Hardy, GH ;

Littlewood, JE .

MATHEMATISCHE ZEITSCHRIFT, 1921, 10 :283-317

← 1 2 3 →