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
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.
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).
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.
