prime number theorem is a key result in this subject. The Mathematics Subject Classification for multiplicative number theory is 11Nxx. Multiplicative number...

differences in technique. Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval...

In quantum field theory, multiplicative quantum numbers are conserved quantum numbers of a special kind. A given quantum number q is said to be additive...

mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible elements...

In number theory, a multiplicative function is an arithmetic function f {\displaystyle f} of a positive integer n {\displaystyle n} with the property...

numbers, and such functions are called multiplicative functions. Outside of number theory, the term "multiplicative function" is often taken to be synonymous...

"Algebraic Number Theory". Retrieved 7 April 2020. Montgomery, Hugh L.; Vaughan, Robert C. (2007). Multiplicative Number Theory: I, Classical Theory. Cambridge...

Terence (10 December 2014). "254A, Notes 2: Complex-analytic multiplicative number theory". Terence Tao's blog. Edwards, Harold M. (2001). Riemann's zeta...

Shapley–Folkman lemma Additive combinatorics Multiplicative combinatorics Multiplicative number theory Nathanson (1996) II:1 Henry Mann (1976). Addition...

and completed his Ph.D. in 1972. His dissertation, Topics in Multiplicative Number Theory, was supervised by Harold Davenport. He became an assistant professor...

Dirichlet convolution of two multiplicative functions is again multiplicative, and every not constantly zero multiplicative function has a Dirichlet inverse...

In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k...

generalizations See Multiplication in group theory, above, and multiplicative group, which for example includes matrix multiplication. A very general, and...

algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the...

Modern Number Theory (2nd ed.). Springer-Verlag. Montgomery, Hugh L.; Vaughan, Robert C. (2006). Multiplicative number theory. I. Classical theory. Cambridge...

interest is in analytic number theory, particularly in the subfields of automorphic L-functions, and multiplicative number theory. Soundararajan grew up...

defined to have a multiplicative identity, while a structure with the same axiomatic definition but without the requirement for a multiplicative identity is...

Retrieved 2025-01-24. "DLMF: §27.2 Functions ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory". dlmf.nist.gov. Retrieved 2025-01-31. Weisstein...

number of primes less than or equal to... "DLMF: §27.12 Asymptotic Formulas: Primes ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory"...

Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication), one of two...

symmetries of IUT: multiplicative arithmetic and additive geometric. On one hand, Hodge theaters generalize such classical objects in number theory as the adeles...

solution, i.e., when it exists, a modular multiplicative inverse is unique: If b and b' are both modular multiplicative inverses of a respect to the modulus...

vu=uv=1,} where 1 is the multiplicative identity; the element v is unique for this property and is called the multiplicative inverse of u. The set of...

a modular multiplicative inverse of a modulo m. If a ≡ b (mod m) and a−1 exists, then a−1 ≡ b−1 (mod m) (compatibility with multiplicative inverse, and...

In number theory, a multiplicative partition or unordered factorization of an integer n {\displaystyle n} is a way of writing n {\displaystyle n} as a...

Introduction to analytic number theory, by K. Chandrasekharan; Arithmetical functions, by K. Chandrasekharan; Multiplicative number theory, by Harold Davenport;...

New Approach to Multiplication and Exponential Functions". In Harel, Guershon; Confrey, Jere (eds.). The Development of Multiplicative Reasoning in the...

2012. Davenport, Harold (2000). Montgomery, Hugh L. (ed.). Multiplicative Number Theory. Graduate Texts in Mathematics. Vol. 74 (3rd ed.). New York:...

Montgomery, Hugh L.; Vaughan, Robert C. (2007). Multiplicative Number Theory. I. Classical theory. Cambridge tracts in advanced mathematics. Vol. 97...

In operator theory, a multiplication operator is a linear operator Tf defined on some vector space of functions and whose value at a function φ is given...