scientific article

Publication date: 5 June 1993

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

survey convolution products sums of squares finite field cyclotomic polynomials number of representations arithmetical functions Ramanujan sums Moebius function periodic functions Ramanujan expansions divisor functions Euler's totient Ramanujan's \(\tau\)-function functions associated with Abelian groups generalizations of multiplicative functions Lehmer's specially multiplicative functions multiplicative functions in two variables

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items

On Ramanujan sums of a real variable and a new Ramanujan expansion for the divisor function ⋮ On an identity of Ramanujan ⋮ Unnamed Item ⋮ An abstract Möbius inversion formula with number-theoretic applications ⋮ Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions ⋮ On Smith's determinant ⋮ Ramanujan sums via generalized Möbius functions and applications ⋮ Distance-regular Cayley graphs on dihedral groups ⋮ A Menon-type identity using Klee's function ⋮ An Euler product transform applied to \(q\)-series ⋮ A variation of the \(q\)-Wolstenholme theorem ⋮ Sums of averages of generalized Ramanujan sums ⋮ Unnamed Item ⋮ Determinant and inverse of join matrices on two sets ⋮ Rademacher Sums and Rademacher Series ⋮ Distributive property of completely multiplicative functions ⋮ Curious congruences for cyclotomic polynomials II ⋮ On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums ⋮ Proofs, generalizations and analogs of Menon's identity: a survey ⋮ A UNIQUE FACTORIZATION IN COMMUTATIVE MÖBIUS MONOIDS ⋮ On partial sums of arithmetical functions of two variables with absolutely convergent Ramanujan expansions ⋮ Combinatorial aspects of the generalized Euler's totient ⋮ Determinant and inverse of meet and join matrices ⋮ Sums of products of Ramanujan sums ⋮ Unnamed Item ⋮ Coefficients and higher order derivatives of cyclotomic polynomials: old and new (with an appendix by Pedro García-Sánchez) ⋮ On the divisibility of meet and join matrices ⋮ Derivation of arithmetical functions under the Dirichlet convolution ⋮ On Ramanujan expansions with multiplicative coefficients ⋮ Sums of averages of gcd-sum functions ⋮ A correspondence between the isobaric ring and multiplicative arithmetic functions ⋮ On a generalization of the Dedekind-Hölder theorem ⋮ An upper bound for the \(\ell_p\) norm of a gcd-related matrix ⋮ Multiple arithmetic functions in function fields ⋮ Independence of additive, multiplicative, exponential and logarithmic functions ⋮ Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs ⋮ Arithmetic functions and the Cauchy product ⋮ On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture ⋮ Ramanujan-Fourier series and a theorem of Ingham ⋮ GENERALIZED ARITHMETICAL FUNCTIONS OF THREE VARIABLES ⋮ Jordan totient quotients ⋮ On the Kesava Menon norm of semimultiplicative functions ⋮ Unitary cyclotomic polynomials ⋮ A note on some characterizations of arithmetic functions ⋮ Dirichlet product and the multiple Dirichlet series over function fields ⋮ A lattice-theoretic approach to the Bourque–Ligh conjecture ⋮ The discrete Fourier transform of \((r, s)\)-even functions ⋮ On the error term in a Parseval type formula in the theory of Ramanujan expansions ⋮ Multiplicative functions and \(k\)-automatic sequences ⋮ On sums of gcd-sum functions ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices