In his 1984 paper Guy Robin showed the Riemann Hypothesis is equivalent to $\sigma(n)\lt e^\gamma n\log\log n$ for all integers $\gt$ 5040.
The Riemann Zeta Function is a special type of L-function which are defined here http://www.lmfdb.org/intro/zetatour
Is there an analog of Robin’s Inequality for a general L-function?