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
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
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...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.展开更多
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 a...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.展开更多
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, ...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.展开更多
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 si...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.展开更多
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 nontr...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.展开更多
Let f(z) be a Hecke-Maass cusp form for SL2(Z), and let L(s, f) be the corresponding automorphic L-function associated to f. For sufficiently large T, let N(σ, T) be the number of zeros p =β + iγ of L(s, ...Let f(z) be a Hecke-Maass cusp form for SL2(Z), and let L(s, f) be the corresponding automorphic L-function associated to f. For sufficiently large T, let N(σ, T) be the number of zeros p =β + iγ of L(s, f) with |γ| ≤T, β〉 σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4≤ σ≤ 1 - ε, there exists a constant C = C(ε) such that N(σ, T) 〈〈 T2(1-σ)/σ(log T)c, which improves the previous results.展开更多
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 ...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.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.
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。
基金supported by National Natural Science Foundation of China(Grant No.11531008)Ministry of Education of China(Grant No.IRT16R43)+3 种基金Taishan Scholar Project of Shandong Provincesupported by National Natural Science Foundation of China(Grant No.11601271)China Postdoctoral Science Foundation(Grant No.2016M602125)China Scholarship Council(Grant No.201706225004)。
文摘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.
文摘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.
基金supported by the Doctorate Foundation of Xi'an Jiaotong University
文摘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.
基金supported by the 973 Programthe National Natural Science Foundation of China (GrantNo. 10531060)+2 种基金Ministry of Education of China (Grant No. 305009)The second author was supportedby the National Security Agency of USA (Grant No. H98230-06-1-0075)The United States government isauthorized to reproduce and distribute reprints notwithstanding any copyright notation herein.
文摘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.
基金supported by the National Basic Research Program of China, the National Natural Science Foundation of China (Grant No. 10531060)Ministry of Education of China (Grant No. 305009)+1 种基金The second author was supported by the National Security Agency (Grant No. H98230-06-1-0075)The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein
文摘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.
基金The author would like to thank Xu Zhao and the referees for carefully reading the manuscript and detailed comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11126151) and the Scientific Foundation of Henan University (Grant No. 2012YBZR030).
文摘Let f(z) be a Hecke-Maass cusp form for SL2(Z), and let L(s, f) be the corresponding automorphic L-function associated to f. For sufficiently large T, let N(σ, T) be the number of zeros p =β + iγ of L(s, f) with |γ| ≤T, β〉 σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4≤ σ≤ 1 - ε, there exists a constant C = C(ε) such that N(σ, T) 〈〈 T2(1-σ)/σ(log T)c, which improves the previous results.
基金supported in part by the Natural Science Foundation of USA (Grant Nos.DMS-0653742,DMS-1001672) and by the Chinese Academy of Sciences
文摘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.