The number of Hecke eigenvalues of same signs

被引：19

作者：

Lau, Y. -K. ^{[2
]}

Wu, J. ^{[1
,3
]}

机构：

[1] Nancy Univ, IECN, CNRS, INRIA, F-54506 Vandoeuvre Les Nancy, France

[2] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[3] Shandong Normal Univ, Inst Math Sci, Jinan 250100, Shandong, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2009年 / 263卷 / 04期

关键词：

Fourier coefficients of modular forms; B-free numbers; CHEBOTAREV DENSITY-THEOREM; FOURIER COEFFICIENTS; SHORT INTERVALS; FORMS;

D O I：

10.1007/s00209-008-0448-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give the best possible lower bounds in order of magnitude for the number of positive and negative Hecke eigenvalues. This improves upon a recent work of Kohnen, Lau and Shparlinski. Also, we study an analogous problem for short intervals.

引用

页码：959 / 970

页数：12

共 23 条

[1] Nonvanishing of Fourier coefficients of newforms in progressions [J].

Alkan, E ;

Zaharescu, A .

ACTA ARITHMETICA, 2005, 116 (01) :81-98

[2]

[Anonymous], 1981, I HAUTES ETUDES SCI

[3] The Chebotarev density theorem in short intervals and some questions of Serre [J].

Balog, A ;

Ono, K .

JOURNAL OF NUMBER THEORY, 2001, 91 (02) :356-371

[4] THE APPROXIMATE FUNCTIONAL EQUATION FOR A CLASS OF ZETA-FUNCTIONS [J].

CHANDRASEKHARAN, K ;

NARASIMHAN, R .

MATHEMATISCHE ANNALEN, 1963, 152 (01) :30-64

[5] The square sieve and the Lang-Trotter conjecture [J].

Cojocaru, AC ;

Fouvry, E ;

Murty, MR .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2005, 57 (06) :1155-1177

[6]

Deligne P., 1981, Publ. Math. IHES., V52, P313

[7]

Deligne P., 1974, PUBL MATH-PARIS, V43, P273, DOI 10.1007/BF02684373

[8]

ELKIES N, 1992, JOURN AR 1989 LUM 19

[9]

ELKIES N, 1991, JOURN AR 1989 LUM 19

[10]

Erdos P., 1966, ACTA ARITH, V12, P175

← 1 2 3 →