Functiones et Approximatio Commentarii Mathematici

Some arithmetic identities involving divisor functions

Şaban Alaca, Faruk Uygul, and Kenneth S. Williams

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For a positive integer $n$, let $\sigma(n):= \sum_{d \in \mathb{N}, d|n} d$. The explicit evaluation of such arithmetic sums as $\sum_{(a,b,c) \in \ABIFnn^3, a+2b+4c=n} \sigma(a)\sigma(b) \sigma(c)$ and $\sum_{(a,b) \in \ABIFnn^2, a+2b=n} a \sigma(a)\sigma(b)$ is carried out for all positive integers $n$.

Article information

Funct. Approx. Comment. Math., Volume 46, Number 2 (2012), 261-271.

First available in Project Euclid: 25 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11F27: Theta series; Weil representation; theta correspondences

sum of divisors function Eisenstein series


Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S. Some arithmetic identities involving divisor functions. Funct. Approx. Comment. Math. 46 (2012), no. 2, 261--271. doi:10.7169/facm/2012.46.2.9.

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