Dušanka Đokić is a notable figure, but no specific widely recognized entity or individual by that name is readily known based on commonly available information as of my last knowledge update in October 2021. There may be specific context, such as cultural or local relevance, that would help clarify who she is.

Matej Pavšič is a name that could refer to various individuals, but without specific context, it's challenging to provide precise information. As of my last knowledge update in October 2021, there may not be widely known notable figures by that name.

Ratko Janev is a Serbian physicist known for his work in atomic and plasma physics, including contributions to the understanding of atomic processes in fusion plasmas. He has published extensively in these fields and is recognized for his research on the interaction of charged particles with matter, which is relevant to both plasma physics and fusion energy research.

The Airy zeta function is a mathematical function that is related to the solutions of the Airy differential equation. The Airy functions, denoted as \( \text{Ai}(x) \) and \( \text{Bi}(x) \), are special functions that arise in various physical problems, particularly in quantum mechanics and wave phenomena, where they describe the behavior of a particle in a linear potential.

Apéry's theorem is a result in number theory that concerns the value of the Riemann zeta function at positive integer values. Specifically, the theorem states that the value \(\zeta(3)\), the Riemann zeta function evaluated at 3, is not a rational number. The theorem was proven by Roger Apéry in 1979 and is significant because it was one of the first results to demonstrate that certain values of the zeta function are irrational.

The arithmetic zeta function, often associated with number theory, is a generalization of the Riemann zeta function, which traditionally sums over integers. The arithmetic zeta function, denoted by \( \zeta(s) \), is defined in various ways depending on the context, typically involving sums or products over prime numbers or algebraic structures. One prominent example of an arithmetic zeta function is the **Dedekind zeta function** associated with a number field.

The Artin conductor is a concept from algebraic number theory, specifically in the study of Galois representations and local fields. It is a tool used to measure the ramification of a prime ideal in the extension of fields, particularly in the context of class field theory.

The Artin–Mazur zeta function is a function associated with a dynamical system, particularly in the context of number theory and arithmetic geometry. It is primarily used in the study of iterative processes and can also be applied to understand the behavior of various types of mathematical objects, such as algebraic varieties and their associated functions over finite fields.

In number theory and representation theory, an automorphic L-function is a type of complex analytic function that encodes significant arithmetic information about automorphic forms, which are certain types of functions defined on algebraic groups over global fields (like the rational numbers) that exhibit certain symmetries and transformation properties. ### Key Concepts: 1. **Automorphic Forms**: These are generalizations of modular forms, defined on the quotient of a group (often the general linear group) over a number field.

The Matsumoto zeta function is a mathematical function that arises in the study of certain types of number-theoretic problems, particularly those related to generalizations of classical zeta functions. It is typically associated with an extension of the classical Riemann zeta function and can be defined for various types of number systems.

The Ramanujan–Petersson conjecture is a significant result in number theory, specifically in the theory of modular forms and automorphic forms. It was formulated by mathematicians Srinivasa Ramanujan and Hans Petersson and deals with the growth rates of the coefficients of certain types of modular forms.

The Rankin-Selberg method is a powerful technique in analytic number theory, used primarily to study L-functions attached to modular forms and automorphic forms. It is named after the mathematicians Robert Rankin and A. Selberg, who developed the theory in the mid-20th century. The method involves the construction of an "intertwining" integral that relates two L-functions.

A Dirichlet character is a complex-valued arithmetic function \( \chi: \mathbb{Z} \to \mathbb{C} \) that arises in number theory, particularly in the study of Dirichlet L-functions and Dirichlet's theorem on primes in arithmetic progressions.

The Eichler–Shimura congruence relations are important results in the field of arithmetic geometry, particularly in the study of modular forms, modular curves, and the arithmetic of elliptic curves. They describe deep relationships between the ranks of certain abelian varieties, specifically abelian varieties that are associated with modular forms.

The Hardy–Littlewood zeta-function conjectures refer to a set of conjectures proposed by mathematicians G.H. Hardy and J.E. Littlewood regarding the distribution of prime numbers and, more broadly, the properties of number-theoretic functions.

The Feller–Tornier constant is a constant that arises in the context of probability theory, particularly in relation to random walks and certain types of stochastic processes. It is named after the mathematicians William Feller and Joseph Tornier, who studied the asymptotic behavior of random walks.

A functional equation is a relation that defines a function in terms of its value at different points, typically revealing symmetries or properties of the function. In the context of L-functions, these are complex functions arising in number theory and are particularly important in areas such as analytic number theory and the theory of modular forms. ### L-functions L-functions are certain complex functions that encode deep arithmetic properties of numbers.

The Generalized Riemann Hypothesis (GRH) is a conjecture in number theory that extends the famous Riemann Hypothesis (RH) beyond the critical line of the Riemann zeta function to other Dirichlet L-functions.

The Igusa zeta function is a mathematical object that arises in number theory and algebraic geometry, particularly in the context of counting points of algebraic varieties over finite fields. It is a generalization of the classical zeta function associated with a variety defined over a finite field. The Igusa zeta function is particularly useful in the study of the solutions of polynomial equations over finite fields.

The Langlands Program is a vast and influential set of conjectures and theories in the fields of number theory and representation theory, proposed by the mathematician Robert Langlands in the late 1960s. It seeks to establish deep connections between different areas of mathematics, notably between: 1. **Number Theory**: The study of integers and their properties. 2. **Representation Theory**: The study of how algebraic structures, like groups, can be represented through linear transformations of vector spaces.