Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,an...Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).展开更多
In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. ...In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.展开更多
L-茶氨酸(L-Theanine,LTA)是茶叶中独特的游离氨基酸,是茶汤鲜爽味的主要来源,具有多种生物活性,属于新食品原料。本文基于Citespace和VOSviewer对Web of Science核心数据库和中国知网数据库,对2014~2024年LTA相关文献进行可视化分析,...L-茶氨酸(L-Theanine,LTA)是茶叶中独特的游离氨基酸,是茶汤鲜爽味的主要来源,具有多种生物活性,属于新食品原料。本文基于Citespace和VOSviewer对Web of Science核心数据库和中国知网数据库,对2014~2024年LTA相关文献进行可视化分析,其中关键词密度和贡献图谱结果显示LTA相关研究集中在茶叶类型、胁迫反应、LTA的生物活性等方面。因此,本文综述了茶叶LTA含量的影响因素,并重点阐述LTA生物活性作用机制,包括抗氧化、抗热应激、抗抑郁、调节代谢、抗癌、调节免疫、调节肠道菌群、保护神经系统、保护肝脏和保护肠道的作用机制,发现LTA主要通过调控核因子κB(Nuclear factor kappa B,NF-κB)、c-Jun氨基末端激酶(c-Jun N-terminal kinase,JNK)、信号传导及转录激活因子(Signal transducer and activator of transcription,STAT)和丝裂原活化蛋白激酶(Mitogen-activated protein kinase,MAPK)等信号通路发挥生物活性功能,并总结了当前LTA在食品产业中的实际应用。本文可为LTA的研究和发展提供方向,并为开发LTA功能性食品提供一定的参考。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
基金Supported by Natural Science Foundation of Shandong Province(No.ZR2024MA053)。
文摘Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).
基金Supported by the National Key R&D Program of China(Grant No.2021YFA1000700)National Natural Science Foundation of China(Grant No.12031008)。
文摘In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.
文摘L-茶氨酸(L-Theanine,LTA)是茶叶中独特的游离氨基酸,是茶汤鲜爽味的主要来源,具有多种生物活性,属于新食品原料。本文基于Citespace和VOSviewer对Web of Science核心数据库和中国知网数据库,对2014~2024年LTA相关文献进行可视化分析,其中关键词密度和贡献图谱结果显示LTA相关研究集中在茶叶类型、胁迫反应、LTA的生物活性等方面。因此,本文综述了茶叶LTA含量的影响因素,并重点阐述LTA生物活性作用机制,包括抗氧化、抗热应激、抗抑郁、调节代谢、抗癌、调节免疫、调节肠道菌群、保护神经系统、保护肝脏和保护肠道的作用机制,发现LTA主要通过调控核因子κB(Nuclear factor kappa B,NF-κB)、c-Jun氨基末端激酶(c-Jun N-terminal kinase,JNK)、信号传导及转录激活因子(Signal transducer and activator of transcription,STAT)和丝裂原活化蛋白激酶(Mitogen-activated protein kinase,MAPK)等信号通路发挥生物活性功能,并总结了当前LTA在食品产业中的实际应用。本文可为LTA的研究和发展提供方向,并为开发LTA功能性食品提供一定的参考。
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.
