On the regularity of arithmetic multiplicative functions, II
نویسندگان
چکیده
منابع مشابه
Alternating Sums Concerning Multiplicative Arithmetic Functions
We deduce asymptotic formulas for the alternating sums ∑ n≤x(−1)f(n) and ∑ n≤x(−1) 1 f(n) , where f is one of the following classical multiplicative arithmetic functions: Euler’s totient function, the Dedekind function, the sum-of-divisors function, the divisor function, the gcd-sum function. We also consider analogs of these functions, which are associated to unitary and exponential divisors, ...
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Let μ be a probability measure on the real line with finite moments of all orders. Suppose the linear span of polynomials is dense in L(μ). Then there exists a sequence {Pn}∞ n=0 of orthogonal polynomials with respect to μ such that Pn is a polynomial of degree n with leading coefficient 1 and the equality (x − αn)Pn(x) = Pn+1(x) + ωnPn−1(x) holds, where αn and ωn are SzegöJacobi parameters. In...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1981
ISSN: 0386-2194
DOI: 10.3792/pjaa.57.130