
	Where results make sense

Topic: Multiplicative function

Related Topics

Dirichlet convolution

Dive bomber

Customer privacy

World Allround Speed Skating Championships

List of New Hampshire rivers

	PlanetMath: multiplicative function
		A multiplicative function is completely determined by its values at the powers of prime numbers, a consequence of the fundamental theorem of arithmetic.
		function is multiplicative, divisor sum of an arithmetic function
		This is version 45 of multiplicative function, born on 2002-06-12, modified 2007-06-23.
	planetmath.org /encyclopedia/MultiplicativeFunction.html (519 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		In this case the function is a homomorphism of monoids and, because of the fundamental theorem of arithmetic, is completely determined by its restriction to the prime numbers.
		A multiplicative function is completely determined by its values at the powers of prime numbers, a consequence of the fundamental theorem of arithmetic.
		With this operation, the set of all multiplicative functions turns into an abelian group; the identity element is ε.
	www.informationgenius.com /encyclopedia/m/mu/multiplicative_function.html (564 words)

	PlanetMath: multiplicative function
		In number theory, a multiplicative function is an arithmetic function
		In other words, every multiplicative function has a convolution inverse that is also multiplicative.
		derivation that divisor function is a multiplicative function
	planetmath.org /encyclopedia/CompletelyMultiplicative.html (519 words)

	Multiplicative function - Wikipedia, the free encyclopedia
		Outside number theory, the term multiplicative is usually used for functions with the property f(ab) = f(a) f(b) for all arguments a and b; this requires either f(1) = 1, or f(a) = 0 for all a except a = 1.
		(n): the divisor function, which is the sum of the k-th powers of all the positive divisors of n (where k may be any complex number).
		Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.
	en.wikipedia.org /wiki/Multiplicative_function (658 words)

	math lessons - Multiplicative function
		In number theory, a multiplicative function is an arithmetic function f(n) of the positive integer n with the property that f(1) = 1 and whenever a and b are coprime, then
		This shows that the function is not multiplicative.
		Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.
	www.mathdaily.com /lessons/Multiplicative_function (619 words)

	Möbius function - Wikipedia, the free encyclopedia
		is an important multiplicative function in number theory and combinatorics.
		This function is closely linked with the positions of zeroes of the Riemann zeta function.
		The classical Möbius function treated in this article is essentially equal to the Möbius function of the set of all positive integers partially ordered by divisibility.
	en.wikipedia.org /wiki/Moebius_function (531 words)

	The Prime Glossary: multiplicative function (Site not responding. Last check: 2007-10-26)
		A function f(n) defined on the positive integers is multiplicative if f(nm)=f(n)f(m) whenever n and m are relatively prime.
		If f(n) is multiplicative and we factor n into distinct primes as n=p
		Finally, if f(n) is multiplicative, then so is the function F(n) = sum of f(i) (where the sum is taken over the divisors i of n).
	primes.utm.edu /glossary/page.php?sort=MultiplicativeFunction (75 words)

	additive function : QuicklyFind Info (Site not responding. Last check: 2007-10-26)
		In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime we have:
		Outside number theory, the term additive is usually used for all functions with the property f(ab) = f(a) + f(b) for all arguments a and b.
		An example of an arithmetic function which is additive but not completely additive is ω(n), defined as the total number of different prime factors of n.
	www.quicklyfind.com /info/additive_function.htm (255 words)

	Analytic Number Theory by Harold Diamond
		This modest requirement imposes significant structure on an arithmetic function, and many interesting functions are either multiplicative or are `nearly so.' We are going to examine several aspects of multiplicative functions, including the following.
		Multiplicative functions will be characterized in terms of convolutions and exponentials of arithmetic functions.
		The summatory function associated with a multiplicative function is often of greater interest than the function itself.
	www.ima.umn.edu /PI/abstracts/diamond1.html (310 words)

	About Smarandache-Multiplicative Functions
		The name of S-multiplicative is a short of Smarandache-multiplicative and reflects the main equation of the Smarandache function.
		Certainly, many properties of multiplicative functions[2] can be translated for S-multiplicative functions.
		The main important property of this function is presented in the following.
	www.gallup.unm.edu /~smarandache/STabirca.htm (193 words)

	Math Forum: MacPOW 967: An Unusual Multiplicative Function
		Suppose f is a function from positive integers to positive integers and
		f is multiplicative (f(mn) = f(m)f(n) when m and n have no common factor)
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /wagon/fall02/p967.html (69 words)

	Publications in the last 3 years (Site not responding. Last check: 2007-10-26)
		B.M. Phong, A characterization of the identity function, Acta Acad.
		A Kovács, B.M. Phong, On additive functions satistying congruence, Ann.
		Kátai, On asymptotically correlated q-multiplicative functions, Mathematicae Pannonica, 10/1 (1999), 29-36.
	compalg.inf.elte.hu /research/PUBDEP.HTML (611 words)

	CSCI 220 Fall 2001 Exam 2 Review (Site not responding. Last check: 2007-10-26)
		Why is table size M = 2^p (p a prime) a bad idea when your hash function is key % M? Why is it a good idea when the hash function is a multiplicative function?
		A hash table of size 2^p when doing mods will cause only the last p bits of the key to be used for the hash function, which makes it more likely that keys will collide (since they're more likely to look the same using only p bits versus all of the bits).
		On the other hand, the multiplicative method munches around the whole number and 2^p as a table size can be used to speed things up.
	cerebro.xu.edu /csci220/01f/exam2Review.html (498 words)

	Math Forum: MacPOW 967: An Unusual Multiplicative Function (Site not responding. Last check: 2007-10-26)
		This problem (in the strong form f(n) = n) was #2 on the morning session of the 1963 Putnam exam.
		Although you say "increasing," you define this as what I would call "strictly increasing." A theorem of Erdos [Ann Math 47 (1946) 1-20] states, more generally, that if f is an increasing multiplicative function, then f(n) = n^k, for some real number k.
		Katai, I. A remark on additive arithmetical functions.
	mathforum.org /wagon/fall02solutions/s967.html (327 words)

	L8.html
		defines the number theoretic function F(n) in terms of the number theoretic function f(d) by summimg f(d) over all positive divisors d of n.
		is multiplicative if the number theoretic function f(n) is multiplicative.
		Actually we have shown that f(n) is more than multiplicative, since we did not need to assume that gcd(a,b)=1.
	www.math.sfu.ca /~gfee/Math342/L81.html (1049 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		/ q = b/a; r = b - aq; if(r == 0) return a; return my_gcd(a,r); } /* In conditional statement form, phi can be defined together with another * function of 2 variables we denote as phiphi.
		= 3 and y > x >= 2 / static int phiphi(int y, int x) { int z; if(x+1 == y)return x; / phi(prime p) = p-1 / if((y%x)==0){ if(my_gcd(x,z=y/x)==1) return phi(x)phi(z); /* multiplicative property / else return xphi(z); /* This is a tricky case.
		It may happen when x is a prime such that a power of x divides y.
	barnyard.syr.edu /quickies/totient.c (261 words)

	Mobius Inversion
		Define the Mobius function to be the unique multiplicative function such that
		be the function that is one on every number.
		don't have to be multiplicative for this to be true.
	www.math.uic.edu /~jeremy/math436/main/node5.html (62 words)

	phi(n) and sigma(n) (Site not responding. Last check: 2007-10-26)
		For any positive integer n, the function div(n) is the number of positive divisors of n, including 1 and n.
		This is also called the Euler totient function.
		Once a number is abundant, all multiples of that number are abundant.
	www.mathreference.com /num,phi.html (430 words)

	Sasa Radomirovic - Math 356 - Number Theory - Summer 2004
		We proved that the Euler Phi function defined on Monday is multiplicative.
		We used the summatory functions of 1 and n to define the number of divisors function and the sum of divisors function as follows
		We proved that the summatory function of a multiplicative function is multiplicative, which immediately implied that τ(n) and σ(n) are multiplicative.
	www.math.rutgers.edu /~sasar/Math356?cd623.txt (408 words)

	Algebraic Properties of Cellular Automata (1984)
		Some values of the multiplicative order function are given in Table 4.
		The multiplicative suborder function is defined as the minimum
		of the multiplicative suborder function is defined as the minimum positive integer
	stephenwolfram.com /publications/articles/ca/84-properties/9/text.html (161 words)

	F_rcase.html
		For an integer n, the definition of the sums of divisors function is
		b) Show that the sums of divisors function is multiplicative
		b) Now we will show that when (m,n) = 1 the sums of the divisors function is multiplicative.
	math.ucsd.edu /~jwavrik/proj107b/F_rcase2.html (102 words)

	Smarandache Functions, Issue 2/2004 Mathematics Magazine
		In this paper we present the definitions and some properties of several Smarandache type functions that are involved in many proposed solved and unsolved problems and conjectures in number theory and recreational mathematics.
		This function has been very much studied in the last decade and interesting properties have been found related to it.
		where S(k) is the classical Smarandache Function, and ÖaØ means the interior integer part of a (the smallest integer greater than or equal to a).
	www.mathematicsmagazine.com /2-2004/SmarTF_2_2004.htm (1651 words)

	ID
		An identity function f is a function which doesn't have any effect: it always returns the same value that was used as its argument.
		is the identity element of the monoid of all functions from M to M.
		When choosing M equal to the positive integers, one obtains the identity function Id(n), which is a multiplicative function considered in number theory.
	www.websters-online-dictionary.com /definition/english/Id/Id.html (3863 words)

	Lecture Summary MP313, Number Theory III
		Euler's phi function, complete set (mod m), the complete set ak+b, gcd(a,m)=1, reduced set (mod m), the reduced set kb, gcd(b,m)=1, solving a linear congruence ax
		Euler-Fermat theorem, summing Euler's function over the divisors of n, two proofs - one involving partitioning, the other via the multiplicative function obtained by summing a given one over the divisors of n, d(n), sigma(n) and perfect numbers.
		Characterisation of even perfect numbers, the Möbius function, summing the Möbius function over the divisors of n (two proofs), the Möbius inversion formula, application to formula for Euler's function, Chinese remainder theorem, 1-1 correspondence between residue classes mod m and the cartesian product of the residue classes mod m
	www.numbertheory.org /courses/MP313/lectures.html (602 words)

	Learn more about Table of divisors in the online encyclopedia. (Site not responding. Last check: 2007-10-26)
		Enter a phrase or search word in the box below.
		You can enter multiple phrases at a time by putting a comma between each word.(e.g.
		Note: multiplicative function d(n): the number of positive divisors of n, including 1 and n itself; σ(n): the sum of all the positive divisors of n, including 1 and n itself.
	www.onlineencyclopedia.org /t/ta/table_of_divisors.html (140 words)

	Möbius function Details, Meaning Möbius function Article and Explanation Guide
		Möbius function Details, Meaning Möbius function Article and Explanation Guide
		Möbius function Guide, Meaning, Facts, Information and Description
		The classical Möbius function μ(n) is an important multiplicative function in number theory and combinatorics.
	www.e-paranoids.com /m/mo/moebius_function.html (547 words)

	Math Forum: MacPOW 967: An Unusual Multiplicative Function (Site not responding. Last check: 2007-10-26)
		Suppose f is a function from positive integers to positive integers and
		f is multiplicative (f(mn) = f(m)f(n) when m and n have no common factor)
		Source: Crux Mathematicorum, Sept. 2002, from a St Petersburg contest.
	mathforum.org /wagon/fall02/p967.html (54 words)

	ABSTRACT ALGEBRA: OnLine Study Guide, Section 6.6
		If d is a positive integer, we define the Moebius function
		If R is a commutative ring, then a function f : Z
		Let R be a commutative ring, and let f : Z
	www.math.niu.edu /~beachy/abstract_algebra/study_guide/66.html (225 words)

Try your search on: Qwika (all wikis)