TY - JOUR
T1 - Monotonicity properties of L-functions
AU - Chaubey, Sneha
AU - Koutsaki, K. Paolina
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2019/6
Y1 - 2019/6
N2 - We present some monotonicity results for a class of Dirichlet series generalizing previously known results. The fact that ζ' (s) 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.
AB - We present some monotonicity results for a class of Dirichlet series generalizing previously known results. The fact that ζ' (s) 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.
KW - 11M06
KW - 11M26
KW - 26A48
KW - Ramanujan-tau L-function
KW - complete monotonicity
KW - first derivative of the Riemann zeta function
KW - logarithmically complete monotonicity
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U2 - 10.1002/mana.201700485
DO - 10.1002/mana.201700485
M3 - Article
AN - SCOPUS:85059190325
SN - 0025-584X
VL - 292
SP - 1238
EP - 1245
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 6
ER -