Number-theoretic functions for Gaussian integers




Gaussian integers, divisor, number of divisors, sum of the divisors, product of the divisors


The classical number-theoretic functions – a number of divisors τ(n), sum of the divisors σ(n) and product of the divisors π(n) of a positive integer n – were generalized to the ring Z[i] of Gaussian integers. For the evaluation of the corresponding functions τ*(α), σ*m(α) and π*(α), obtained were the explicit formulae that use the canonical representation of α. A number of properties of these functions were studied, in particular, estimates from above for the functions τ*(α) and σ*m(α) and the properties connected with divisibility of their values by certain numbers. Researched are also sums of products of powers of the divisors for α∈Z[i].

Pages of the article in the issue: 11 - 20

Language of the article: English


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How to Cite

Arskyi, N. (2023). Number-theoretic functions for Gaussian integers. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 11–20.



Algebra, Geometry and Probability Theory