ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r)
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Publication:3173466
DOI10.1142/S179304211100437XzbMath1273.11052arXiv0808.4118OpenAlexW2161745378MaRDI QIDQ3173466
Publication date: 10 October 2011
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0808.4118
arithmetic progressiontensor productDirichlet's theoremMertens' theoremDirichlet convolutionCauchy's interlacing inequalitiescompletely even function (mod r)
Other Dirichlet series and zeta functions (11M41) Matrices of integers (15B36) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)
Related Items (25)
Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ On a certain determinant for a U.F.D. ⋮ Divisibility among power matrices associated with classes of arithmetic functions ⋮ 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 ⋮ Multiple divisor chains and determinants of matrices associated with completely even functions (modr) ⋮ On the divisibility among power GCD and power LCM matrices on gcd-closed sets ⋮ Determinant and inverse of join matrices on two sets ⋮ Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains ⋮ MORE ON A CERTAIN ARITHMETICAL DETERMINANT ⋮ On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices ⋮ On a certain arithmetical determinant ⋮ Further results on generalized LCM matrices ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ Bounds on the spectrum of nonsingular triangular \((0,1)\)-matrices ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ On the eigenvalues of combined meet and join matrices ⋮ Divisibility properties of power GCD matrices and power LCM matrices ⋮ A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix ⋮ Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets ⋮ GCD-closed sets and divisibility of Smith matrices ⋮ A lattice-theoretic approach to the Bourque–Ligh conjecture ⋮ 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
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