Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to...

concentration Abstract analytic number theory, the application of ideas and techniques from analytic number theory to other mathematical fields Analytic combinatorics...

the largest proper divisor of n can be no larger than ⁠n/2⁠. Abstract analytic number theory for information about generalizations of the theorem. Landau...

titles. Abstract analytic number theory The study of arithmetic semigroups as a means to extend notions from classical analytic number theory. Abstract differential...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation...

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of...

{\log(X)}})),\,} where cK is a constant depending on K. Abstract analytic number theory Alina Carmen Cojocaru; M. Ram Murty (8 December 2005). An introduction...

demonstrated. In proof theory, the notion of analytic proof provides the fundamental concept that brings out the similarities between a number of essentially...

came from number theory, geometry, analysis, and the solutions of algebraic equations. Most theories that are now recognized as parts of abstract algebra...

Abstract Analytic Number Theory (2nd ed.). New York: Dover. ISBN 0-486-66344-2. Zbl 0743.11002. Nathanson, Melvyn B. (1996). Additive Number Theory: the Classical...

Analytic philosophy is a broad movement within Western philosophy, especially anglophone philosophy, focused on analysis as a philosophical method. It...

questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several...

an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions...

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations...

by either analytic methods such as Liouville's theorem, or topological ones such as the winding number, or a proof combining Galois theory and the fact...

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation...

approximation) Ax–Kochen theorem (number theory) Baker's theorem (number theory) Barban–Davenport–Halberstam theorem (analytic number theory) Basel problem (mathematical...

primes, but if γ = 3/2 then this conclusion need not hold. Abstract analytic number theory Bateman, Paul T.; Diamond, Harold G. (1969), "Asymptotic distribution...

applications in other areas including abstract algebra, number theory, and the analysis of algorithms. Analytic Combinatorics is not primarily a textbook;...

introduced the fundamental idea of analytic proof to proof theory. Structural proof theory is the subdiscipline of proof theory that studies the specifics of...

A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,...

One key achievement of this abstract algebraic geometry is Grothendieck's scheme theory which allows one to use sheaf theory to study algebraic varieties...

(1) Concepts are abstract objects, and (2) concepts are mental representations. Within the framework of the representational theory of mind, the structural...

generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the...

Neumann and Claude Shannon. Automata theory is the study of abstract machines (or more appropriately, abstract 'mathematical' machines or systems) and...

incorporates the bijective approach and various tools in analysis and analytic number theory and has connections with statistical mechanics. Partitions can be...

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical...

in this general perspective, are analytic functionals quantifying the invariance of number fields in a most abstract sense, therefore indicating the 'primitivity'...

with analytical mechanics in the old sense now expressed in terms of symplectic topology, based on the newer theory of manifolds. The term theory is used...