2 problems

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Dyer–Harman conjecture on the greatest-common-divisor sum
For an increasing sequence $(n_k)$ of integers, consider the estimate … where $(n_k,n_l)$ denotes the greatest common divisor and $c$ is the constant occurring in the estimate. Dye…
Conjectureopenanalytic-number-theory gcd-sums probabilistic-number-theoryarXiv posted 3 days ago
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Extension of the GCD-sum estimate to the endpoint α = 1/2
Let $g(\alpha,N)$ be the function in Theorem, defined for $0<\alpha<1$ , and consider the corresponding GCD-sum estimate for arbitrary $N$ -tuples of distinct positive integers. Endp…
Conjectureopenanalytic-number-theory gcd-sums harmonic-analysisarXiv posted 3 days ago

Dyer–Harman conjecture on the greatest-common-divisor sum