Monotonicity properties of ‐functions
Copyright policy )Monotonicity properties of ‐functions
AbstractWe present some monotonicity results for a class of Dirichlet series generalizing previously known results. The fact that is in that class presents a first example of an arithmetic function for which the associated Dirichlet series is completely monotonic, but not logarithmically completely monotonic. Lastly, we use similar techniques to prove another formulation of the Riemann hypothesis for the L‐function associated to the Ramanujan‐tau function.
- University of Illinois at Urbana Champaign United States
- Romanian Academy Romania
- Western Illinois University United States
- Indraprastha Institute of Information Technology Delhi India
- University of Illinois at Urbana–Champaign United States
Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, first derivative of the Riemann zeta function, Ramanujan-tau \(L\)-function, \(\zeta (s)\) and \(L(s, \chi)\), complete monotonicity, logarithmically complete monotonicity
Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, first derivative of the Riemann zeta function, Ramanujan-tau \(L\)-function, \(\zeta (s)\) and \(L(s, \chi)\), complete monotonicity, logarithmically complete monotonicity
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