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2 votes
1 answer
162 views

Closed form expression for this zeta-like series involving GCD and LCM

I am looking for a closed form for this function $\Lambda:\mathbb{Q}^+\to\mathbb{R}^+$: $$\Lambda(q) = \sum_{m,n\geq 1}\left(\frac{q\wedge\frac{m}{n}}{q\vee\frac{m}{n}}\right)^\alpha\left(\frac{m \...
Alexandre's user avatar
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3 votes
1 answer
437 views

Is there a Riemann Hypothesis criterion utilizing sum of squares of divisors?

Robin's inequality $$\sigma_1(n)<e^\gamma n\log\log n$$ at integers $n>5040$ provides necessary and sufficient condition for Riemann Hypothesis where $\sigma_1(n)=\sum_{d|n}d$ is sum of divisors ...
Turbo's user avatar
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