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Evaluation of divisor functions of matrices

Gautami Bhowmik (1996)

Acta Arithmetica

1. Introduction. The study of divisor functions of matrices arose legitimately in the context of arithmetic of matrices, and the question of the number of (possibly weighted) inequivalent factorizations of an integer matrix was asked. However, till now only partial answers were available. Nanda [6] evaluated the case of prime matrices and Narang [7] gave an evaluation for 2×2 matrices. We obtained a recursion in the size of the matrices and the weights of the divisors [1,2] which helped us obtain...

Examples of ε-exhaustive pathological submeasures

Ilijas Farah (2004)

Fundamenta Mathematicae

For any given ε > 0 we construct an ε-exhaustive normalized pathological submeasure. To this end we use potentially exhaustive submeasures and barriers of finite subsets of ℕ.

Existence and reduction of generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

Luis M. Navas, Francisco J. Ruiz, Juan L. Varona (2019)

Archivum Mathematicum

One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the “main family” those given by 2 λ e t + 1 α e x t = ∑ n = 0 ∞ ℰ n ( α ) ( x ; λ ) t n n ! , λ ∈ ℂ ∖ { - 1 } , and as an “exceptional family”...

Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions

István Mező (2013)

Open Mathematics

There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli, Gosper and Srivastava. In this paper, we extend some of them. Namely, we give the exponential generating function of hyperharmonic numbers indexed by arithmetic progressions; in the sum several combinatorial numbers (like Stirling and Bell numbers) and the hypergeometric function appear.

Extended finite operator calculus-an example of algebraization of analysis

Andrzej Kwaśniewski, Ewa Borak (2004)

Open Mathematics

“A Calculus of Sequences” started in 1936 by Ward constitutes the general scheme for extensions of classical operator calculus of Rota-Mullin considered by many afterwards and after Ward. Because of the notation we shall call the Ward's calculus of sequences in its afterwards elaborated form-a ψ-calculus. The ψ-calculus in parts appears to be almost automatic, natural extension of classical operator calculus of Rota-Mullin or equivalently-of umbral calculus of Roman and Rota. At the same time this...

Extended Ramsey theory for words representing rationals

Vassiliki Farmaki, Andreas Koutsogiannis (2013)

Fundamenta Mathematicae

Ramsey theory for words over a finite alphabet was unified in the work of Carlson, who also presented a method to extend the theory to words over an infinite alphabet, but subject to a fixed dominating principle. In the present work we establish an extension of Carlson's approach to countable ordinals and Schreier-type families developing an extended Ramsey theory for dominated words over a doubly infinite alphabet (in fact for ω-ℤ*-located words), and we apply this theory, exploiting the Budak-Işik-Pym...

Currently displaying 81 – 100 of 109