Grand Zero Density Estimates of L-functions Associated with Cusp Forms

In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L f (s,χ),where f is a holomorphic cusp form and χ a Dirichlet character of mod q.

Double square moments and subconvexity bounds for Rankin-Selberg L-functions of holomorphic cusp forms

Let f and g be holomorphic cusp forms of weights k1 and k2 for the congruence subgroups TO(N1)and Γ0(N2),respectively.In this paper the square moment of the Rankin-Selberg L-function for f and g in the aspect of both weights in short intervals is bounded,when k1^ε <<k^2<<k1^1-ε.These bounds are the mean Lindelof hypothesis in one case and subconvexity bounds on average in other cases.These square moment estimates also imply subconvexity bounds for individual L(1/2+it,f×g) for all g when f is chosen outside a small exceptional set.In the best case scenario the subconvexity bound obtained reaches the Weyl-type bound proved by Lau et al.(2006) in both the k1 and k2 aspects.

The Cancellation of Fourier Coefficients of Cusp Forms over Different Sparse Sequences

Abstract Let λf（n） be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f（z） ∈ Sk（F）, In this paper, we established nontrivial estimates for ∑n≤x λf（n^i）λf（n^j）,where 1≤ij≤4.

On the Third and Fourth Power Moments of Fourier Coefficients of Cusp Forms

The asymptotic formulae for the third and fourth power moments of Fourier coefficients of cusp forms are proved in this paper.

Quadratic forms connected with Fourier coefficients of Maass cusp forms

For the normalized Fourier coefficients of Maass cusp forms λ（n） and the normalized Fourier coefficients of holomorphic cusp forms a（n）, we give the bound of

On the Distribution and Moments of the Fourier Coefficients of Cusp Forms

Two theorems about the distribution and moments of the Fourier coefficients of cusp forms are proved in this paper.

On the Fourth Power Moment of Fourier Coefficients of Cusp Form

Let a（n） be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A（x） =∑n≤xa（n）.In this paper, we establish an asymptotic formula of tile fourth power moment of A（x） and prove that ∫1^TA^4（x）dx=3/64κπ^4s4;2（a^~）T^2κ＋O（T^2a-δ4＋t） with δ4 = 1/8, which improves the previous result.

Exponential Sums over Primes Formed with Coefficients of Primitive Cusp Forms

Let Af（n） be the coefficient of the logarithmic derivative for the Hecke L-function. In this paper we study the cancellation of the function Ay（n） twisted with an additive character e（α√n）, α 〉0, i.e. Ef（x） = Σx〈n〈2x Af（n）e（α√n）.

Sums of Fourier coefficients of cusp forms of level D twisted by exponential functions

Let g be a holomorphic or Maass Hecke newform of level D and nebentypus XD, and let ag（n） be its n-th Fourier coefficient. We consider the sum S1=∑ X〈n≤2x ag（n）e（an β） and prove that S1 has an asymptotic formula when β = 1/2 and α is close to ±2 √q/D for positive integer q ≤ X/4and X sufficiently large. And when 0 〈β 〈 1 and α, β fail to meet the above condition, we obtain upper bounds of S1. We also consider the sum S2 = ∑n〉0 ag（n）e（an β） Ф（n/X） with Ф（x） ∈ C c ∞（0,＋∞） and prove that S2 has better upper bounds than S1 at some special α and β.

Dimension formula of cusp form spaces on half-spaces of quaternions

A dimension formula for the cusp form spaces defined on half-spaces of quaternions by Selberg trace formula is deduced and the contributions of several conjugacy classes to dimension formula are calculated.

On shifted convolution of half-integral weight cusp forms

In this note,we present a simple approach for bounding the shifted convolution sum involving the Fourier coefficients of half-integral weight holomorphic cusp forms and Maass cusp forms.

Maass形式的傅里叶系数在算术级数中的渐近性

自守形式理论是现代数论的重要课题.自守形式的傅里叶系数蕴含了深刻的数论性质,其在数论中有许多应用.设f是本原Maass尖形式,λ_(f)(n)是它在尖点无穷远处的第n个傅里叶系数.结合经典的解析方法和一些本原自守L-函数的性质,本文研究了全模群上Maass尖形式的傅里叶系数在算术级数上的分布性质,得到了相应的渐近公式.

Representations by Certain Sextenary Quadratic Forms Whose Coefficients Are 1, 2, 3 and 6

Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.

Bounds for Average toward the Resonance Barrier for GL(3)×GL(2)Automorphic Forms

Let f be a fixed Maass form for SL_3(Z)with Fourier coefficients A_(f)(m,n).Let g be a Maass cusp form for SL_2(G)with Laplace eigenvalue(1/4)+k^(2) and Fourier coefficientλ_(g)(n),or a holomorphic cusp form of even weight k.Denote by S_(X)(f×g,α,β)a smoothly weighted sum of A_(f)(1,n)λ_(g)(n)e(αn~β)for X 0 are fixed real numbers.The subject matter of the present paper is to prove non-trivial bounds for a sum of S_(X)(f×g,α,β)over g as k tends to∞with X.These bounds for average provide insight for the corresponding resonance barriers toward the Hypothesis S as proposed by Iwaniec,Luo,and Sarnak.

螺旋面截形尖点矢量离散法及其在双圆弧滚刀过渡曲面最小化中的应用

在具有尖点廓形的螺旋曲面成形加工中,计算出的刀具截形常常产生曲线自交叉现象,导致刀具加工出的螺旋曲面在尖点处生成较大的过渡曲面。为此,提出尖点矢量离散法,将点及其法向矢量定义为一个点矢量,对两相交曲线在尖点处形成的首尾两个点矢量进行离散,使尖点处更多的几何信息带入到廓形计算中,提高了计算精度。给出过渡曲面最小化算法,用工件截形离散尖点矢量及两侧四个点矢量计算刀具廓形点,消除自交叉后得到刀具尖点及附近四个点;用刀具点反算工件廓形点,得到过渡曲线;通过所建立的过渡曲面大小评价标准,以过渡曲线最小为目标在一定范围内进行刀具安装角优化。将该方法应用于双圆弧齿轮滚刀的铲磨加工中,通过实际加工验证,表明该方法可有效降低过渡曲面的大小,适用于具有尖点廓形的螺旋曲面成形加工的计算优化。

椭圆元在维数公式中的贡献

主要算出SU(n,1)中正规椭圆元g的共轭类在维效公式中的贡献: N(g)=λn-(n+1)m/|C(g)|(λ-λ1)(λ-λ2)…(λ-λn),其中m≥2,Bn表示n维超球,SU(n,1)是Bn的自同构群且在Bn上可迁;不失一般性,上式中g=对角阵(λ1,…,λn,λ)(其中λi≠λ,i=1,2,…,n)．

非线性单主元企业组织规模发展的突变分析

该文简述了突变现象的研究,探讨了突变的内涵;讨论了影响企业组织规模的因素;从定性的角度对企业组织规模发展的突变作了研究,从定量方面给出了非线性企业组织规模的一般函数,探讨了它的近似问题;结合例子,应用突变理论,对企业组织规模发展的折叠型、尖点型突变进行了分析。

非线性单主元企业组织规模发展的突变点判定

本文简要阐述了突变现象的研究,探讨了突变的形式和突变点寻找所涉及的问题。通过对影响企业组织规模因素的讨论,给出了非线性企业组织规模的一般函数。探讨了非线性单主元企业组织规模函数的近似问题。结合例子,应用突变理论,就其折叠型、尖点型的突变判定进行了研究,并就突变点寻找的方法作了小结。

A Zero Density Estimate for Automorphic L-functions

1 Introduction Let f be a holomorphic cusp form for the group F = SL2（Z） of even integral weight k, with Fourier coefficients af （n）.