# On A New Multiplicative Function

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### On the Structure of the Group of Multiplicative Arithmetical

by PO Dehaye 2002 Cited by 7 Let F0 denote the set of all multiplicative functions different from 0. Clearly, f(1) = 1 for every f ∈ F0. The Dirichlet product (or convolution) of two arithmetical

### On a new multiplicative function - IOPscience

by MA Korolev 1998 Cited by 3 COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY. On a new multiplicative function. To cite this article: M A Korolev 1998 Russ. Math. Surv.

### Some Properties of Completely Multiplicative Arithmetical

by TM Apostol 1971 Cited by 40 Modern Algebra, Ungar, New York, 1953, vol. 1, Ch. 4 and 5. SOME PROPERTIES OF COMPLETELY MULTIPLICATIVE. ARITHMETICAL FUNCTIONS.

### Multiplicative functions in arithmetic progressions

by A BALOG Cited by 24 MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS primes in the arithmetic progressions (modq), albeit rather different from what we had.

### MULTIPLICATIVE NUMBER-THEORETIC FUNCTIONS AND

The following theorems, which are easily proved by several different methods, give the formula for ¢ (n) and for the sum of ¢ (n) over the divisors of n. Theorem 2.6.

### Multiplicative arithmetic functions

The functions τ and σ just defined are multiplicative arithmetical functions. Indeed, if m = The total number of known Mersenne primes is 48 (the latest being.

### EXPLICIT AVERAGES OF NON-NEGATIVE MULTIPLICATIVE

by O RAMARÉ Cited by 9 Evaluating the average of multiplicative functions is a classical and important prob- lem. It has been When K0 ≥ K, this new sum is empty. But since if (k, q1)

### DISTRIBUTION OF MULTIPLICATIVE FUNCTIONS - Annales

by J Galambos Cited by 4 from their proof one obtains the validity of the following result, which is itself new in this form. Theorem 4. Let g(m) = 0. Then g(m) has a limit distribution function.

### Multiplicative functions and operators of Hecke - AKJournals

interesting examples of 0-multiplicative functions, however. These include the plicative set of operators, and this leads to a new interpretation of Theorem 5. 4.

### Injectiveness and Discontinuity of Multiplicative - MDPI

by P Jiménez-Rodríguez 2021 multiplicative convex function is at most 2-injective, and construct proposed a different way to define multiplicative convexity were the aim

### Completely multiplicative functions with sum zero - CentAUR

by AA Neamah 2020 Cited by 1 functions tends to zero with different generalised prime systems. The findings of this paper may suggest that for all CMOP functions f over N with abscissa 1, we

### MULTIPLICATIVE FUNCTIONS IN ARITHMETIC

by A Balog Cited by 24 We develop a theory of multiplicative functions (with values inside or on the unit arithmetic progressions mod q, albeit rather different from what we had

### Mean values of multiplicative functions over function - CORE

by A Granville 2015 Cited by 7 Abstract. We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors' new proof of Halász's theorem on mean

### The Spectrum of Multiplicative Functions - JSTOR

by A Granville 2001 Cited by 48 By applying this corollary to the completely multiplicative function f (n) = the only new and interesting case is where o- = 1, which gives the logarithmic.

### 3.4 Multiplicative Functions - The University of Manchester

Question how to identify a multiplicative function? If it is the convolution of two other arithmetic functions we can use. Theorem 3.19 If f and g are multiplicative

### s mean value Theorem for Multiplicative Functions - London

by A Hildebrand 1986 Cited by 23 any real-valued multiplicative function / of modulus < 1 has a mean value, that is, functions. We shall give here a new elementary proof of Wirsing's theorem in

### A NEW PROOF OF ERDOS'STHEOREM ON MONOTONE

by E HOWE Cited by 6 The following remarkable theorem concerning increasing multiplicative functions is due to Erdos. [21. THEOREM.I f f is increasing and multiplicative, then there is a

### COMPLETELY MULTIPLICATIVE FUNCTIONS ARISING

by V LAOHAKOSOL Cited by 7 Given two multiplicative arithmetic functions, various conditions for their convolution, J. Riordan, Combinatorial Identities, John Wiley & Sons, New York, 1968.

### TOTALLY MULTIPLICATIVE FUNCTIONS IN REGULAR

by KL Yocom 1973 Cited by 34 for an arithmetic function to be totally multiplicative to the incidence (and some apparently new ones) to the regular convolution rings of

### CLUSTERING OF LINEAR COMBINATIONS OF

by N Lebowitz-Lockard 2017 Cited by 1 of multiplicative functions to be nonclustering, meaning not clustering anywhere. This provides a means of generating new families of arithmetic functions

### The structure of multiplicative functions with small - arXiv

by D Koukoulopoulos 2019 Cited by 1 partial sums of a multiplicative function whose average value on primes is If m ≤ D denotes the multiplicity, then a new application of Taylor's

### On Quasi Multiplicative Function

Abstract In this paper we introduce two new Arithmetic functions, that is, Quasi-Multiplicative (QM) and omega. ( )ω functions. The Omega ( )ω function is based

### DIRICHLET PRODUCT OF DERIVATIVE ARITHMETIC WITH

by ES En-Naoui 2019 A function f is called an multiplicative function if and only if : convolution f ∗ g is a new arithmetic function defined by: (f ∗ g)(n) = ∑ d n f(d)g(.

### Klurman, O. (2017). Correlations of multiplicative functions

by O Klurman Cited by 33 n = a+b where a, b belong to some multiplicative subsets of N. This gives a new circle method-free proof of the result of Brüdern. 1. Introduction. Let U denote

### Multiplicative functions in short intervals, and - IMPA

We will be interested throughout in multiplicative functions, that is f : N ! C The main new idea in the proof of Theorem 6 is an iterative scheme, factoring out

### Exponential sums with multiplicative coefficients - Deep Blue

by RC Vaughan 1977 Cited by 180 multipticative functions f such that I f(p)[ < A for all primes p and. N. If(n)lZ

### Topics in Multiplicative and Probabilistic Number Theory by

by AP Mangerel 2018 Cited by 1 In a different direction, we consider the collection of periodic, completely multiplicative functions, also known as Dirichlet characters.

### MULTIPLICATIVE FUNCTIONS: A REWRITE OF ANDREWS

Each function is multiplicative, in the sense defined below. Definition We are now going to see how to build a new multiplicative function from an old one.

### REMARKS ON MULTIPLICATIVE FUNCTIONS Atle Selberg

by A Selberg 1977 Cited by 29 Institute for Advanced Study, Princeton~ New Jersey 08540 functions according to our new definition° define multiplicative functions of several variables.

### A Structure Theorem for Level Sets of Multiplicative Functions

by V Bergelson 2020 Cited by 5 We also show that if a level set E of a multiplicative function has positive J) ∩ J = ∅ for all n ∈ N. We define a new multiplicative function g as.

### 762 THE IDENTICAL EQUATIONS OF THE MULTIPLICATIVE

by R Vaidyanathaswamy 1930 Cited by 16 1. Introduction. An arithmetic function ƒ(N) is multiplicative, If f(N) and yp(M , M2) are multiplicative functions, it is clear that we have different ways. In the first

### Multiplicative functions and k-automatic sequences - Numdam

by S Yazdani 2001 Cited by 14 0. Also combining Theorems 1 and 2 we get the following new result. Corollary 10. For all integers v, rrz, k > 2 the sequences (Tm(n) mod V)

### LINEAR CORRELATIONS OF MULTIPLICATIVE FUNCTIONS

by L MATTHIESEN Cited by 15 We prove a Green Tao theorem for multiplicative functions. Contents. 1. Inserting the new expressions for χ and λ at all instances in (6.2) (resp. (6.3)) and.

### ANALYTIC NUMBER THEORY AND DIRICHLET'S THEOREM

by J BINDER 2008 An arithmetic function f is called a multiplicative function if, are finitely many; multiply them all together and add one; the new quantity is not.

### Math 406 Section 7.1: Multiplicative Functions - UMD MATH

(a) Definition: A function is arithmetic if it is defined for all positive integers. (b) Definition: An arithmetic function f is multiplicative if f(mn) = f(m)f(n) whenever.

### When Does the Bombieri Vinogradov Theorem Hold for a

by A Granville 2018 Cited by 5 Right click to open a feedback form in a new tab to let us know how this Let f and g be 1-bounded multiplicative functions for which f ∗ g = 1.

### A New Proof of Erdos's Theorem on Monotone Multiplicative

by E Howe 1986 Cited by 6 f(n) = na for alln >1. THEOREM B. Every increasing multiplicative function is completely multiplicative. 2. Proof of Theorem A. Let f be increasing and completely

### Almost multiplicative functionals - SIUE

by K Jarosz Cited by 34 B is a product of finitely many interpolating Blaschke products then. 1. Introduction. Let G be a linear and multiplicative functional on a Banach algebra A and let.

### THE THEORY OF MULTIPLICATIVE ARITHMETIC FUNCTIONS*

by R Vaidyanathaswamy 1931 Cited by 130 Journal of the Indian Mathematical Society, pointing out the fact (which I then believed to be new) that every multiplicative function of a single argu-.

### A structure theorem for multiplicative functions and applications

Structure theorem for multiplicative functions on the integers: χ(n) = χst New partition regularity results Key tool: A structural result for multiplicative functions.

### ON THE PROXIMITY OF MULTIPLICATIVE FUNCTIONS TO

by JM De Koninck 2018 Cited by 1 Given an additive function f and a multiplicative function g, let E(f, g; x) = #{n ≤ x : f(n) = g(n)}. Observing that, with this new radius r1, we get. 1. 2πi. ∫. z =r1.

### Multiplicative functions (M16)

by A Walker claim to understand the properties of the integers under multiplication if we proving extremely surprising new results on multiplicative functions themselves.

### ON THE MEAN VALUE OF NONNEGATIVE MULTIPLICATIVE

by P Erdös Cited by 14 A multiplicative function g(n) is called strongly multiplicative if for all primes and all positive integers A Renyi, A new proof of a theorem of Delange, Publ. Math.

### Harmonic Analysis on the Positive Rationals II: Multiplicative

by PDTA Elliott 2016 Cited by 11 The emphasis is, however, quite different. 2. Multiplicative Functions. A systematic study of multiplicative functions with values in the complex unit disc, initiated by

### ON THE CORRELATION OF COMPLETELY MULTIPLICATIVE

by HS Ganguli 2013 Cited by 2 In the next two chapters we will study this weaker conjecture and prove a number of new results in this direction. Page 18. Chapter 2. Liouville function on Integer.

### General multiplicative functions

by IZ EtrasA strongly multiplicative function f plays the same role here as the charac- ters in the proof is different, but we prove it through a similar lemma. by condition (C).

### Möbius Inversion Formula. Multiplicative Functions - Berkeley

by Z Stankova-Frenkel Counting the elements in D in two different ways implies n = ∑d n. ϕ(d). We can use this Remark to show again multiplicativity of the Euler function: indeed, this

### A note on Helson's conjecture on moments of - Caltech

by AJ Harper Cited by 21 Rademacher random variables), and define a multiplicative function modulo different primes in the moment computation, whereas the geometric factor

### CHARACTERIZING COMPLETELY MULTIPLICATIVE

by V Laohakosol Cited by 14 terizations of completely multiplicative functions are given; save a minor Because of the different nature of the methods, the proof of Theorem

### On the Almost Periodic Behavior of Multiplicative Number

functions requires especial care. The limit process which leads to the given multiplicative function is formally more involved than, though in principle iot different