On Hecke eigenvalues at Piatetski-Shapiro primes

被引：5

作者：

Baier, Stephan ^{[1
]}

Zhao, Liangyi ^{[2
]}

机构：

[1] Jacobs Univ, Sch Sci & Engn, D-28725 Bremen, Germany

[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 81卷

关键词：

NUMBER THEOREM; EXPONENTIAL-SUMS; COEFFICIENTS; MONOMIALS;

D O I：

10.1112/jlms/jdp064

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(n) be the normalized nth Fourier coefficient of a holomorphic cusp form for the full modular group. We show that, for some constant C > 0 depending on the cusp form and every fixed c in the range 1 < c < 8/7, the mean value of lambda(p) is O (exp (-C root log N)) as p runs over all (Piatetski-Shapiro) primes of the form [n(c)] with n is an element of N and n <= N.

引用

页码：175 / 201

页数：27

共 30 条

[11]

Heath-Brown DR, 2001, ACTA MATH-DJURSHOLM, V186, P1

[12] THE PJATECKII-SAPIRO PRIME NUMBER THEOREM [J].

HEATHBROWN, DR .

JOURNAL OF NUMBER THEORY, 1983, 16 (02) :242-266

[13]

Iwaniec H., 2004, Amer. Math. Soc. Colloq. Publ., V53

[14]

Iwaniec H., 2001, Inst. Hautes tudes Sci. Publ. Math, V91, P55, DOI [DOI 10.1007/BF02698741, 10.1007/BF02698741]

[15]

JIA CH, 1993, SCI CHINA SER A, V36, P913

[16]

JIA CH, 1994, CHINESE ANN MATH B, V15, P9

[17]

JIA CH, 1994, CHINESE ANN MATH B, V15, P123

[18]

Jutila M., 1987, TATA I FUNDAMENTAL R, V80

[19] PRIMES OF THE FORM [NC] [J].

KOLESNIK, G .

PACIFIC JOURNAL OF MATHEMATICS, 1985, 118 (02) :437-447

[20]

Kolesnik G., 1969, MAT ZAMETKI, V6, P545

← 1 2 3 →