Results 51 to 60 of about 12,228,153 (333)
On an arithmetic triangle of numbers arising from inverses of analytic functions. [PDF]
, 2018 The Lagrange inversion formula is a fundamental tool in combinatorics. In this work, we investigate an inversion formula for analytic functions, which does not require taking limits.
Bagdasaryan, Armen G., Bagdasar, Ovidiu
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Divisibility of arithmetic functions [PDF]
Pacific Journal of Mathematics, 1984 A derivative-like operator on the Dirichlet ring of arithmetic functions is used to develop formulas for the greatest common divisor of certain arithmetic functions. It is conjectured that formulas of this type hold more generally.
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Function Interval Arithmetic [PDF]
, 2014 We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1 ...
Jan Duracz +3 more
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On a certain class of arithmetic functions [PDF]
Mathematica Bohemica, 2017 A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in\mathbb{N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general.
Antonio M. Oller-Marcén
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On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L‐functions in the Selberg class [PDF]
Journal of the London Mathematical Society, 2015 We establish the equivalence of conjectures concerning the pair correlation of zeros of L ‐functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals.
H. Bui, J. Keating, D. Smith
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A Functional Equation in Arithmetic [PDF]
Transactions of the American Mathematical Society, 1936 which occurs in all theories of numerical functions hitherto considered. The two most highly developed theories of this kind are those in which multiplication in the ring of all numerical functions is abstractly identical with C (Cauchy) or D (Dirichlet) multiplication of infinite series.t Lehmer's five postulates are sufficient for the development of ...
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Higher moments of arithmetic functions in short intervals: a geometric perspective [PDF]
, 2016 We study the geometry associated to the distribution of certain arithmetic functions, including the von Mangoldt function and the M\"obius function, in short intervals of polynomials over a finite field $\mathbb{F}_q$.
D. Hast, Vlad Matei
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On values of arithmetical functions at factorials [PDF]
, 1993 The Smarandache function is a characterization of factorials, since S(k!) = k, and is connected to values of other arithmetical functions at ...
Sandor, J.
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Arithmetic functions associated with infinitary divisors of an integer
International Journal of Mathematics and Mathematical Sciences, 1993 The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y.
Graeme L. Cohen, Peter Hagis
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A NOTE ON EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS [PDF]
, 2006 Let n > 1 be a positive ...
Sandor, J.
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