Sums of divisors of the ternary quadratic with almost equal variables

It is proved that the sum ∑|mi−x|≤xθd(m12+m22+m32) has an asymptotic formula with θ=12+2ϵ. Moreover, we prove that this sum has a more refined asymptotic formula for θ=67+ϵ.

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Bibliographic Details
Published in:Journal of number theory 2015-10, Vol.155, p.248-263
Main Authors: Hu, Liqun, Yao, Yanjun
Format: Article
Language:English
Subjects:
Circle method
Divisor of the ternary quadratic
Exponential sum in short intervals
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Description
Summary:It is proved that the sum ∑|mi−x|≤xθd(m12+m22+m32) has an asymptotic formula with θ=12+2ϵ. Moreover, we prove that this sum has a more refined asymptotic formula for θ=67+ϵ.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2015.03.018