Value Distribution Of L-functions Research Articles

Weighted Value Sharing and Uniqueness Problems Concerning L-Functions and Certain Meromorphic Functions

The purpose of the paper is to study the uniqueness problem of an L function in the Selberg class sharing one or two sets with an arbitrary meromorphic function having only finitely many poles. We manipulate the notion of weighted sharing of sets to improve a result of Q.Q. Yuan, X.M. Li, and H.X. Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249–262, 2018]. Most importantly, we have pointed out a number of logical shortcomings in the two results of P. Sahoo and S. Haldar [Results on L functions and certain uniqueness question of Gross, Lith. Math. J., 60(1):80–91, 2020]. As an attempt to rectify the results of Sahoo and Halder, we have improved them by presenting their accurate forms and proofs as far as practicable.

Results on L-functions and certain uniqueness questions of Gross

In this paper, we study the value distribution of L-functions in the Selberg class and concentrate on the uniqueness questions of L-functions that share one or two sets with an arbitrary meromorphic function. The results obtained in this paper improve the recent results due to Q.-Q. Yuan, X.-M. Li, and H.-X. Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249–262, 2018] and also extend a result due to B.Q. Li [A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071–2077, 2010].

Value distribution of L-functions and uniqueness questions of F. Gross*

We study the value distribution of L-functions and uniqueness questions of meromorphic functions sharing one or two sets with L-functions. The results in this paper extend the corresponding results from [J. Steuding, Value Distribution of L-Functions, Lect. Notes Math., Vol. 1877, Springer-Verlag, Berlin, Heidelberg, 2007, p. 152] and [B.Q. Li, A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071–2077, 2010]. The studied questions in this paper are related to the questions of Gross from [F. Gross, Factorization of meromorphic functions and some open problems, in Complex Analysis, Kentucky 1976. Proceedings of the Conference Held at the University of Kentucky, May 18–22, 1976, Lect. Notes Math., Vol. 599, Springer-Verlag, Berlin, Heidelberg, 1977, pp. 51–69]. Here the meromorphic functions are of finitely many poles in the complex plane.

Further results on value distribution of L-functions

Further results on value distribution of L-functions

Value distribution of L-functions concerning shared values and certain differential polynomials

In this paper, we study a uniqueness question of meromorphic functions of certain differential polynomials that share a nonzero finite value or have the same fixed points with the same of L-functions. The results in this paper extend the corresponding results from Steuding [12, p. 152], Li [7], Fang [1] and Yang-Hua [14].

Value distribution of L-functions concerning sharing sets

We use the concept of set centroid to study the value distribution of L-functions in the (extended) Selberg class, which shows how an L-function and a meromorphic function are uniquely determined by their two sharing sets. The results in this paper extend Theorem 1 in Li [A result on value distribution of L-functions, Proc. Amer. Math. Soc., 138(2010):2071-2077]. In addition, we show the accuracy of the results by giving some examples.

On the Number of Zeros of Linear Combinations of Independent Characteristic Polynomials of Random Unitary Matrices

We show that almost all the zeros of any finite linear combination of inde- pendent characteristic polynomials of random unitary matrices lie on the unit circle. This result is the random matrix analogue of an earlier result by Bombieri and Hejhal on the distribution of zeros of linear combinations of L-functions, thus providing further evidence for the conjectured links between the value distribution of the characteristic polynomial of random unitary matrices and the value distribution of L-functions on the critical line.

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.

On the value distribution of L-functions of the Selberg class

In this paper, two limit theorems in the sense of the weak convergence of probability measures in the space of meromorphic functions and on the complex plane are proved for L-functions from a subclass of the Selberg class. The explicit form of the limit measures is given.

A result on value distribution of L-functions

A result on value distribution of L-functions