On the usual product of rational arithmetic functions
Cauchy multiplication and periodic functions (mod r).
We analise periodic functions (mod r), keeping Cauchy multiplication as the basic tool, and pay particular attention to even functions (mod r) having the property f(n) = f((n,r)) for all n. We provide some new aspects into the Hilbert space structure of even functions (mod r) and make use of linera transformations to interpret the known number-theoretic formulae involving solutions of congruences.
Studying the various properties of MIN and MAX matrices - elementary vs. more advanced methods
Let T = {z1, z2, . . . , zn} be a finite multiset of real numbers, where z1 ≤ z2 ≤ · · · ≤ zn. The purpose of this article is to study the different properties of MIN and MAX matrices of the set T with min(zi , zj) and max(zi , zj) as their ij entries, respectively.We are going to do this by interpreting these matrices as so-called meet and join matrices and by applying some known results for meet and join matrices. Once the theorems are found with the aid of advanced methods, we also consider whether...
Some characterizations of specially multiplicative functions.
On the norm of GCD and related matrices.
An upper bound for the norm of a gcd-related matrix.
On the maximum row and column sum norm of GCD and related matrices.
On generalized Landau identities.
Some characterizations of totients.
Errata to: Comparison of regular convolutions.
A property of generalized Ramanujan's sums concerning generalized completely multiplicative functions.
An identity for a class of arithmetical functions of several variables.
On an inequality related to the Legendre totient function.
Comparison of regular convolutions
Bounds for sine and cosine via eigenvalue estimation
Define n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the first super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the first super- and subdiagonal are minus one. Then, denoting by λ(·) the largest eigenvalue, [...] Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain...
On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix
Consider the recursion g0 = a, g1 = b, gn = gn−1 + gn−2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn−1. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general.
Notes on the divisibility of GCD and LCM matrices.
Determinant and inverse of meet and join matrices.
Sums of values of even functions
Page 1