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）.

UNIQUENESS THEOREMS OF L-FUNCTIONS IN THE EXTENDED SELBERG CLASS

We establish uniqueness theorems of L-functions in the extended Selberg class,which show how an L-function and a meromorphic function are uniquely determined by their shared values in two finite sets.This can be seen as a new solution of a problem proposed by Gross.

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.

Value Distribution of L-Functions with Rational Moving Targets

We prove some value-distribution results for a class of L-functions with rational moving targets. The class contains Selberg class, as well as the Riemann-zeta function.

强直性脊柱炎模型小鼠踝关节组织和临床患者PBMC中miR-142-5p,SOCS1 mRNA表达及与免疫功能分析研究

目的探究强直性脊柱炎(ankylosing spondylitis,AS)模型小鼠和临床患者外周血单个核细胞(peripheralblood mononuclear cell,PBMC)中微小RNA-142-5p(miR-142-5p),细胞因子信号转导抑制因子1(suppressor ofcytokine signaling 1,SOCS1)mRNA表达及其对免疫功能的影响。方法通过实时荧光定量(quantitative real timePCR,qRT-PCR)检测2022年1月~2023年3月商丘市第一人民医院收治的30例确诊的AS患者(患者组)和30例健康体检者(健康组)的PBMC中miR-142-5p和SOCS1 mRNA水平。采用牛蛋白聚糖联合完全弗氏佐剂诱导AS小鼠模型,然后将小鼠分为对照组、模型组、阴性组和拮抗剂组。对照组和模型组小鼠尾静脉注射生理盐水,阴性组和拮抗剂组小鼠分别尾静脉注射NC-antagomir和miR-142-5p-antagomir。治疗2周后,分别评估各组小鼠的关节炎症状评分。通过苏木精伊红(hematoxylin eosin,HE)染色评价踝关节形态。采用ELISA法检测小鼠血清中Th1细胞因子干扰素γ(IFN-γ)、Th2细胞因子白细胞介素-4(IL-4)、Th17细胞因子白细胞介素-17(IL-17)和Treg细胞因子叉头盒蛋白P3(FOXP3)的表达水平。通过qRT-PCR和Western blot检测PBMC和踝关节组织中miR-142-5p,SOCS1,IFN-γ,IL-4,IL-17和FOXP3的mRNA和蛋白表达水平。结果与健康组比较,患者组PBMC中miR-142-5p水平升高(3.03±0.99 vs1.00±0.21),SOCS1 mRNA水平降低(0.41±0.09 vs 1.00±0.18),差异具有统计学意义(t=10.997,15.956,均P<0.001)。与对照组比较,模型组小鼠踝关节组织中miR-142-5p水平(4.00±0.52 vs 1.00±0.04)升高,IFN-γ和IL-17的mRNA和蛋白水平均升高,SOCS1,IL-4和FOXP3的mRNA和蛋白水平均降低,差异具有统计学意义(t=23.356,31.420,48.056,47.224,38.035,29.007,54.183,28.123,55.155,26.758,45.346,均P<0.05);关节炎症状评分升高(7.83±0.94 vs 0.00±0.00,t=22.212,P<0.05),踝关节结构破坏明显;血清中IFN-γ,IL-17水平以及IFN-γ/IL-4比值(0.81±0.08 vs 2.08±0.33)和IL-17/FOXP3比值(0.41±0.03 vs 1.27±0.10)均升高,差异具有统计学意义(t=15.382,35.779,15.412,35.130,均P<0.05)。与阴性组比较,拮抗剂组小鼠踝关节组织中miR-142-5p水平(1.47±0.10 vs 3.89±0.33)降低,IFN-γ和IL-17的mRNA和蛋白水平均降低,SOCS1,IL-4和FOXP3的mRNA和蛋白水平均升高,差异具有统计学意义(t=18.846,22.969,43.454,32.617,23.259,20.881,41.832,11.994,32.977,15.190,35.834,均P<0.05);关节炎症状评分降低(7.42±1.24 vs 2.75±0.75,t=13.233,P<0.05),踝关节形态明显改善;血清中IFN-γ,IL-17水平以及IFN-γ/IL-4比值(1.22±0.11 vs 1.91±0.19)和IL-17/FOXP3比值(0.69±0.05vs 1.23±0.12)均降低,差异具有统计学意义(t=8.688,22.972,8.377,22.007,均P<0.05)。结论miR-142-5p在AS中高表达,使用拮抗剂下调miR-142-5p可能通过上调SOCS1进而降低Th1/Th2和Th17/Treg比值,从而改善AS小鼠的免疫平衡并抑制AS的进展。

苦瓜皂苷L调控PI3K/AKT通路促进内皮祖细胞增殖能力和内皮功能的实验研究

目的:探讨苦瓜皂苷L对内皮祖细胞(EPC)增殖能力和内皮功能的作用及机制。方法:体外分离、培养、鉴定外周血EPC。使用不同浓度苦瓜皂苷L处理EPC 24 h后,应用细胞计数试剂盒(CCK-8)法检测各组细胞活力。使用AutoDock Tools 5.6软件,分别以磷脂酰肌醇3-激酶(PI3K)和蛋白激酶B(AKT)为受体,以药物分子苦瓜皂苷L为配体采用盲对接法进行分子对接。使用PI3K/AKT抑制剂LY294002和最佳使用浓度的苦瓜皂苷L单独或同时处理EPC 24 h后检测各组细胞活力和磷酸化PI3K(p-PI3K)、磷酸化AKT(p-AKT)及磷酸化内皮型一氧化氮合酶(p-eNOS)表达水平。结果:与对照组比较,苦瓜皂苷L呈剂量依赖性地促进EPC增殖,且40μmol/L的苦瓜皂苷L是最佳药物浓度。与对照组比较,LY294002可下调EPC细胞活力,苦瓜皂苷L可上调细胞活力。与苦瓜皂苷L组比较,共同使用苦瓜皂苷L和LY294002可降低细胞活力。分子对接结果显示,苦瓜皂苷L与PI3K和AKT均存在直接作用,形成稳定的锁钥结构。与对照组比较,LY294002可显著下调p-PI3K、p-AKT和p-eNOS蛋白水平;苦瓜皂苷L可上调p-PI3K、p-AKT和p-eNOS蛋白水平。与苦瓜皂苷L组比较,使用苦瓜皂苷L和LY294002可降低p-PI3K、p-AKT和p-eNOS蛋白水平。结论:苦瓜皂苷L通过PI3K/AKT信号通路靶向调节EPC的增殖能力,进而上调内皮型一氧化氮合酶(eNOS)活化水平以促进EPC内皮功能。

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.

桑树基因组学研究进展

栽桑养蚕的历史对整个人类文明产生了重要的影响。桑树是多年生木本植物,具有重要的经济价值、药用价值和生态价值。自2013年桑树基因组测序项目实施以来,桑树的研究进入了基因组学时代,为桑树的分子育种奠定了基础。本文从桑树基因组测序的实施开始,系统总结了桑树基因组学研究的最新进展,包括了测序技术、拼接策略、组装质量以及基于全基因组重测序应用等方面。未来,随着技术的不断创新,桑树基因组学研究将迎来更广阔的发展前景。本文旨在推动桑树产业的发展并为林木基因组学的研究提供理论与技术参考。

A New Zero-density Result of L-functions Attached to Maass Forms

Let f denote a normalized Maass cusp form for SL（2, Z）, which is an eigenfunction of all the Hecke operators T（n） as well as the reflection operator T-1： z →z. We obtain a zero-density result of the L-function attached to f near σ = 1. This improves substantially the previous results in this direction.

枸杞子在我国保健食品中的应用

枸杞子属于食药同源物质,富含多糖、甜菜碱、花色苷、类胡萝卜素等活性成分,在免疫力提升、缓解视疲劳、抗氧化等保健功能中具有良好的应用价值,也因此受到了国内外研究者和消费者的喜爱。目前,枸杞子在我国保健食品中的应用频率较高,但缺乏系统的整理和分析。基于此,本文分析了枸杞子在我国保健食品中的应用现状、合规性使用依据、主要功效成分的影响因素,并详细论述了枸杞子主要的保健功能和作用机制,以期为枸杞子在我国保健食品中的研究开发和应用提供一定的参考及依据。

On the 2k-th Power Mean of Inversion of L-functions with the Weight of the Gauss Sum

The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.

Correlation of zeros of automorphic L-functions

We compute the n-level correlation of normalized nontrivial zeros of a product of L-functions:L(s,π1)···L(s,πk), where πj, j=1,...,k, are automorphic cuspidal representations of GLmj(QA). Here the sizes of the groups GLmj(QA) are not necessarily the same. When these L(s,πj) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s,πj) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m1,...,mk 4,but are under Hypothesis H in other cases.

Functoriality of automorphic L-functions through their zeros

Let E be a Galois extension of Q of degree , not necessarily solvable. In this paper we first prove that the L-function L(s,π) attached to an automorphic cuspidal representation π of GLm(EA) cannot be factored nontrivially into a product of L-functions over E. Next, we compare the n-level correlation of normalized nontrivial zeros of L(s,π1)···L(s,πk), where πj, j = 1,...,k, are automorphic cuspidal representations of GLmj(QA), with that of L(s,π). We prove a necessary condition for L(s,π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific GLmj(QA), j = 1,...,k. In particular, if π is not invariant under the action of any nontrivial σ∈ GalE/Q, then L(s,π) must equal a single L-function attached to a cuspidal representation of GLm (QA) and π has an automorphic induction, provided L(s,π) can factored into a product of L-functions over Q. As E is not assumed to be solvable over Q, our results are beyond the scope of the current theory of base change and automorphic induction. Our results are unconditional when m,m1,...,mk are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.

基于自由曲面和L-system的红掌生长模型

针对红掌花卉生长可视化中参数难以确定的问题进行研究,提出推导控制点的方法,建立红掌器官模型:采用Bezier曲线结合扫描成型的方法来构造叶柄模型,采用双三次NURBS曲线对佛焰苞进行建模;运用红掌的相关表型数据拟合生长函数,提出基于红掌生长规律的微分L-system,可有效模拟红掌的拓扑结构和生长过程;通过虚拟器官表示红掌器官的几何属性,降低微分L-system的复杂度。试验验证提出的方法对红掌各项生长指标拟合度可达0.89以上,并可对每个生长阶段的红掌进行模拟,能有效地对红掌的生长过程进行建模。

Periods of automorphic forms,poles of L-functions and functorial lifting

In this paper,we survey our work on period,poles or special values of certain automorphic Lfunctions and their relations to certain types of Langlands functorial transfers.We outline proofs for some results and leave others as conjectures.

余甘子提取物及其复配物改善大鼠的功能性消化不良症状

该研究通过《保健食品功能检验与评价方法(2022年版)》中的促进消化功能检验方法中小鼠小肠运动、大鼠增重、摄食量、食物利用率、胃蛋白酶测定等试验研究了余甘子单方和四种复方的促消化效果。结果表明,余甘子(单方组),余甘子、山楂、茯苓和陈皮(复方1组),余甘子、山楂、白术和麦芽(复方2组),余甘子、山楂、茯苓、白术和陈皮(复方3组),余甘子、山楂、茯苓、白术、麦芽和陈皮(复方4组)小鼠小肠推进率分别提高了65.99%、80.53%、107.91%、67.47%、90.47%(P<0.05,P<0.01,P<0.0001,P<0.05,P<0.001),大鼠胃蛋白酶活性分别增强了89.24%、60.42%、103.07%、74.56%、106.84%(P<0.01,P≥0.05,P<0.01,P<0.05,P<0.01),大鼠胃蛋白酶排出量分别增强了89.30%、60.39%、103.14%、74.69%、106.98%(P<0.01,P≥0.05,P<0.01,P<0.05,P<0.01)。此外,复方4组大鼠食物利用率增加了15.35%(P<0.05),体质量增长、摄食量无显著差异(P≥0.05),其他组别的上述3项指标均无显著影响(P≥0.05)。研究表明余甘子提取物及其复配物可有效改善大鼠功能性消化不良症状。该研究为余甘子及其复配物促消化功能产品的开发和推广提供了相应的理论参考。

A NEW MEAN VALUE FORMULA OF DIRICHLET'S L-FUNCTIONS

By using the estimates of the character sums and the Bombieri-Vinogradov’s theorem, anew mean value formula of Dirichlet’s L--functions is derived.

Zero-density Estimates for Automorphic L-functions

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

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.

一个二元多项式的Mahler测度

将一个二元多项式P(x,y)=(x2+1)y2+2(x2+x)y+x(x2+1)的Mahler测度表达成一些Bloch-Wigner双对数函数的线性和,进而得到其与χ-3的L函数特殊值的有理倍数关系:m(P(x,y))=5/2L′(X_(-3),-1)。