Displaying similar documents to “On the convergence and summability of series with respect to block-orthonormal systems.”

Sign changes of error terms related to arithmetical functions

Paulo J. Almeida (2007)

Journal de Théorie des Nombres de Bordeaux

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Let H ( x ) = n x φ ( n ) n - 6 π 2 x . Motivated by a conjecture of Erdös, Lau developed a new method and proved that # { n T : H ( n ) H ( n + 1 ) < 0 } T . We consider arithmetical functions f ( n ) = d n b d d whose summation can be expressed as n x f ( n ) = α x + P ( log ( x ) ) + E ( x ) , where P ( x ) is a polynomial, E ( x ) = - n y ( x ) b n n ψ x n + o ( 1 ) and ψ ( x ) = x - x - 1 / 2 . We generalize Lau’s method and prove results about the number of sign changes for these error terms.