| 尖点形式L函数的零点密度估计(Ⅱ) |
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| 引用本文： | 李英杰,于晓爽.尖点形式L函数的零点密度估计(Ⅱ)[J].安徽大学学报(自然科学版),2010,34(6). |
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| 作者姓名： | 李英杰 于晓爽 |
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| 基金项目： | 国家自然科学基金，上海高校选拔培养优秀青年教师科研专项基金，上海海洋大学博士科研启动基金 |
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| 摘 要： | 设k为一正偶数,T是充分大的正数,s=σ+it,3≤Q=T,q为一正整数,χ是模q的特征,f(z)=∞∑n=1a(n)e2πinz为Γ=SL2(z)的权为k的全纯尖点形式.设Nf(σ0,T,χ)表示函数Lf(s,χ)=∞∑n=1χ(n)a(n)n-s在带形区域k/2+(l/(log(Q2T))≤σ0≤σ≤((k+1)/2),|t|≤T内的零点个数.当k/2+1/3≤σ0≤((k+1)/2)时,由Dirichlet多项式理论得出了∑q≤Q∑χmodqNf(σ0,T,χ)的一个上界.
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| 关 键 词： | 尖点形式 L函数 零点密度 |
Zero density estimates of L-functions associated with cusp forms(II) |
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| LI Ying-jie,YU Xiao-shuang.Zero density estimates of L-functions associated with cusp forms(II)[J].Journal of Anhui University(Natural Sciences),2010,34(6). |
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| Authors: | LI Ying-jie YU Xiao-shuang |
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| Abstract: | Suppose k be a positive even integer,T was a sufficiently large positive number.Let s = σ + it,3≤Q = T.Let q be a positive integer and χ a Dirichlet character mod q.f(z) = ∞∑n=1 a(n) e2πinz was a holomorphic cusp form of weight k with respect to Γ = SL2(z) .Let Nf(σ0,T,χ) denoted the total number of zeros of Lf(s,χ) = ∞∑ n = 1χ(n) a(n) n-s in the region k/2 +(l/(log(Q2T)) ≤σ0 ≤σ≤((k+1)/2),| t | ≤T.An upper bound was given for the sum ∑q≤Q χm∑od qNf(σ0,T,χ) for k/2 + 1/3 ≤σ0 ≤((k+1)/2)by the theories of Dirichlet polynomials. |
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| Keywords: | cusp form L-function zero density |
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