In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficien...Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).展开更多
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 ...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.展开更多
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.
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.
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)m...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。展开更多
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
文摘Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).
基金the National Natural Science Foundation of China(11301076,11571288 and 11971401)the Natural Science Foundation of Fujian Province,China(2018J01658).
文摘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.
基金Supported by the NNSF of China（11071186）Supported by the Science Foundation for the Excellent Youth Scholars of Shanghai（ssc08017）Supported by the Doctoral Research Fund of Shanghai Ocean University
文摘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.
文摘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.
文摘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。
