Integral mean square estimation for the error term involving divisor functions of integer matrices
The asymptotic behaviour of the number of representations of integer matri-ces is an important topic in analytic number theory,and has received increasing attention.Let t3(2)(n)be a summatory function of the number of representations of matrices from the ring of integer matrices M2(Z)in the form C=A1A2A3 with|C|=n.Denote byΔ*2,3(x)the error term of asymptotic formula related to t(2)3(n).Applying the classical analytic method and nice properties of the Riemann zeta function,this paper investigates the distribution of divisor functions of integer matrices t(2)3(n)on the square-free numbers and obtains the upper bounds for the integral mean square of error terms Δ*2,3(x).
error termsquare-free numberdivisor function of integer matrix
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