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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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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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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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Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic

ACM Transactions on Mathematical Software, 1992
Ping Tak Peter Tang
exaly  

Computing the Lambert W function in arbitrary-precision complex interval arithmetic

Numerical Algorithms, 2019
Fredrik Johansson, Johansson Fredrik
exaly  

Arithmetical Functions and Minimalization

Mathematical Logic Quarterly, 1974
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