Results 301 to 310 of about 12,228,153 (333)

Additive Arithmetic Functions on Arithmetic Progressions

Proceedings of the London Mathematical Society, 1987
For an additive arithmetic function f, and positive integer D, let E(x,D) be \[ \max_{y\leq x}\max_{(r,D)=1}| \sum_{n\leq y,\quad n\equiv r (mod D)}f(n)-(1/\phi (D))\sum_{n\leq y,\quad (n,D)=1}f(n)|. \] Strengthening results from Chapter 7 of his monograph ''Arithmetic functions and integer products'' (1985; Zbl 0559.10032), the author proves that for ...
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Inequalities involving arithmetic functions

Lithuanian Mathematical Journal
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic ...
Stoyan Dimitrov
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On Arithmetical Shift for Walsh Functions

IEEE Transactions on Computers, 1972
A general expression for oo such that cal (k,θ+θ0)= sal (k,θ) is obtained and a proof is given. This new form of θ0 is more direct and thus easier to use than other existing formulas.
Chon Tam Le Dinh, Roger Y. Goulet
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Arithmetical Functions and Distributivity

Canadian Mathematical Bulletin, 1970
In this note we shall present a result about incidence functions on a locally finite partially ordered set, a result which is related to theorems of Lambek [2] and Subbarao [6]. Our terminology and notation will be that of Smith [4, 5] and Rota [7].Let (L, ≤) be a partially ordered set which is locally finite in the sense that for all x, y ∊ L the ...
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Multiplicative Arithmetic Functions of Several Variables: A Survey

, 2013
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd convolution. We
L. Tóth
semanticscholar   +1 more source

Arithmetic Functions

Number Theory and its Applications, 2021
S. Kundu, Sypriyo Mazumder
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Function Evaluation in Unnormalized Arithmetic

Journal of the ACM, 1964
The evaluation of a function of one argument is a standard computational task. When an unnormalized number representation is used, it is appropriate that function evaluation to subject to certain “adjustment” criteria, defined independently of the computing method. In this paper some such criteria are developed, and their application described.
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Arithmetical Functions

1994
The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related ...
Wolfgang Schwarz, Jürgen Spilker
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Arithmetical functions. I

The author plans a series of three articles on the theory of arithmetical functions, of which the present one is the first. The paper is expository at the introductory level. This first part deals with some problems of elementary number theory.
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Mean values for a class of arithmetic functions in short intervals

Mathematische Nachrichten, 2020
Jie Wu
exaly