Small values of the Euler function and the Riemann hypothesis
The author studies the function NEWLINE\[NEWLINEc(n)= \Biggl({n\over\varphi(n)}- e^\gamma\log\log n\Biggr)\sqrt{\log n}.NEWLINE\]NEWLINE He proves that several explicit bounds for \(c(n)\) are equivalent to the Riemann hypothesis. One of these upper bounds is NEWLINE\[NEWLINEc(n)\leq c\Biggl(\prod_{1\leq k\leq 66} p_k\Biggr)= 4,06\dots;NEWLINE\]NEWLINE here \(p_1< p_2<\cdots\) denotes the series of primes.
scientific article; zbMATH DE number 6090471