TWISTED L-FUNCTIONS OVER NUMBER FIELDS AND HILBERT'S ELEVENTH PROBLEM

被引：34
|
作者：
Blomer, Valentin [1 ]
Harcos, Gergely [2 ]
机构：
[1] Math Inst, D-37073 Gottingen, Germany
[2] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2010年 / 20卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Subconvexity; ternary quadratic forms; shifted convolution sums; spectral decomposition; Hilbert modular forms; Kirillov model; HALF-INTEGRAL WEIGHT; FOURIER COEFFICIENTS; MODULAR-FORMS; QUADRATIC-FORMS; ZETA; EQUIDISTRIBUTION; POINTS; VALUES; SERIES; BOUNDS;
D O I：
10.1007/s00039-010-0063-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let K be a totally real number field, p an irreducible cuspidal representation of GL(2)(K)\GL(2)(AK) with unitary central character, and. a Hecke character of conductor q. Then L(1/2, pi circle times chi) << (Nq)(1/2-1/8(1 - 2 theta)+epsilon), where 0 <= theta <= 1/2 is any exponent towards the Ramanujan-Petersson conjecture (theta = 1/9 is admissible). The proof is based on a spectral decomposition of shifted convolution sums and a generalized Kuznetsov formula.
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页码：1 / 52
页数：52
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