The 𝜏 (𝛼) function on the integer gaussian with fixed amount of the prime divisors
Journal Title: Дослідження в математиці і механіці - Year 2015, Vol 20, Issue 1
Abstract
The distribution of the divisor’s function’s values 𝜏 (𝛼) over 𝑍[𝑖] in the arithmetical progressions with the growing progression’s difference was analized in present work. The asymptotic formulae for the sum function, which is associated with multiplicated function 𝑧𝑤(𝛼) in narrow segment 𝑁(𝛼) 6 𝑥, 𝜙1 6 arg 𝛼 6 𝜙2, where 𝑤(𝛼) is the amount of different prime divisors of 𝛼 was built here. The result is the non-trivial asymptotic formulae for the sum of the values 𝜏 (𝛼) in narrow segment with the fixed amount of prime divisors.
Authors and Affiliations
V. E. Breide, A. S. Radova
Keywords
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