## 147 Citations

### Universality and distribution of zeros and poles of some zeta functions

- MathematicsJournal d'Analyse Mathématique
- 2020

This paper studies zeta functions of the form $$\sum\nolimits_{n = 1}^\infty {\chi (n){n^{- s}}}$$ ∑ n = 1 ∞ χ ( n ) n − s , with χ a completely multiplicative function taking only unimodular values.…

### On the Theory of Zeta-functions and L-functions

- Mathematics
- 2015

In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results…

### A survey on the theory of universality for zeta and $L$-functions

- Mathematics
- 2014

We survey the results and the methods in the theory of universality for various zeta and $L$-functions, obtained in these forty years after the first discovery of the universality for the Riemann…

### The joint universality of twisted automorphic $L$-functions

- Mathematics
- 2004

The simultaneous universality of twisted automorphic L-functions, associated with a new form with respect to a congruence subgroup of SL(2; Z) and twisted by Dirichlet characters, is proved.…

### Value-distribution of the Riemann zeta-function and related functions near the critical line

- Mathematics
- 2014

We study the value-distribution of the Riemann zeta-function and related functions on and near the critical line. Amongst others, we focus on the following:
The critical line is a natural boundary…

### On joint universality for derivatives of the Riemann zeta function and automorphic $L$-functions (Functions in Number Theory and Their Probabilistic Aspects)

- Mathematics
- 2012

In this paper we establish two results. The first result looks like a joint universality theorem for a set of derivatives of the Riemann zeta function. The second result is a joint universality…

### The joint universality theorem for automorphic $L$-functions (Analytic Number Theory : related Multiple aspects of Arithmetic Functions)

- Mathematics
- 2012

is dense in the set $\mathbb{C}$ of all complex numbers. In 1975, S. M. Voronin [15] extended this denseness result to the infinite dimensional space, that is, the functional space and obtained the…

### Erratum to: The generalized strong recurrence for non-zero rational parameters

- Mathematics
- 2012

In the present paper, we prove that self-approximation of $${\log \zeta (s)}$$ with d = 0 is equivalent to the Riemann Hypothesis. Next, we show self-approximation of $${\log \zeta (s)}$$ with…

### Universality of $L$-Functions over function fields

- Mathematics
- 2018

We prove that the Dirichlet $L$-functions associated with Dirichlet characters in $\mathbb{F}_{q}[x]$ are universal. That is, given a modulus of high enough degree, $L$-functions with characters to…

## References

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### Recursive properties of transformation groups. II

- Mathematics
- 1946

The purpose of this note is to sharpen a previous result on the transmission of recursive properties of a transformation group to certain of its subgroups. [See Recursive properties of transformation…

### Uniform distribution of sequences

- Mathematics
- 1974

( 1 ) {xn}z= Xn--Z_I Zin-Ztn-I is uniformly distributed mod 1, i.e., if ( 2 ) lim (1/N)A(x, N, {xn}z)-x (0x<_ 1), where A(x, N, {Xn)) denotes the number of indices n, l<=n<=N such that {x} is less…

### Real and complex analysis

- Mathematics
- 1966

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures…