Arithmetical properties of generalized Ramanujan sums
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Publication:2548980
DOI10.2140/pjm.1972.41.281zbMath0226.10045OpenAlexW1964823596MaRDI QIDQ2548980
Publication date: 1972
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2140/pjm.1972.41.281
Other Dirichlet series and zeta functions (11M41) Arithmetic functions; related numbers; inversion formulas (11A25)
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Factorization theorems for relatively prime divisor sums, GCD sums and generalized Ramanujan sums ⋮ Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r) ⋮ On a certain determinant for a U.F.D. ⋮ Divisibility among power matrices associated with classes of arithmetic functions ⋮ Hyperdeterminants on meet-semilattices ⋮ Divisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ On Smith's determinant ⋮ On the polynomial Ramanujan sums over finite fields ⋮ Multiple divisor chains and determinants of matrices associated with completely even functions (modr) ⋮ Sums of averages of generalized Ramanujan sums ⋮ Unnamed Item ⋮ On the divisibility among power GCD and power LCM matrices on gcd-closed sets ⋮ Greatest common divisor matrices ⋮ Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains ⋮ Unnamed Item ⋮ Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm ⋮ Zeta functions of quadratic Artin–Schreier curves in characteristic two ⋮ MORE ON A CERTAIN ARITHMETICAL DETERMINANT ⋮ On a certain arithmetical determinant ⋮ ASYMPTOTIC BEHAVIOR OF LARGEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (MOD r) ⋮ THERE DOES NOT EXIST AN ODD SINGULAR NUMBER OF THE FORM plqr ⋮ Divisibility of matrices associated with multiplicative functions ⋮ Hyperdeterminants associated with multiple even functions ⋮ On a general form of meet matrices associated with incidence functions ⋮ An analogue of Ramanujan's sum with respect to regular integers (mod \(r\)) ⋮ Notes on Hong's conjectures of real number power LCM matrices ⋮ Divisibility properties of power GCD matrices and power LCM matrices ⋮ On GCD and LCM matrices ⋮ Sums of averages of gcd-sum functions ⋮ Another generalisation of smith's determinant ⋮ Arithmetical properties of multiple Ramanujan sums ⋮ Nonsingularity of matrices associated with classes of arithmetical functions ⋮ Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets ⋮ GCD matrices, posets, and nonintersecting paths ⋮ Maximum nullity of some Cayley graphs ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Power GCD Matrices for a UFD ⋮ On sums of generalized Ramanujan sums ⋮ On the divisibility of power LCM matrices by power GCD matrices ⋮ GCD-closed sets and divisibility of Smith matrices ⋮ Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ Nonsingularity of least common multiple matrices on gcd-closed sets ⋮ On Nonsingular Power LCM Matrices ⋮ On the Bourque-Ligh conjecture of least common multiple matrices ⋮ On sums of gcd-sum functions
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