A discrete mean-value theorem for the higher derivatives of the Riemann zeta function
نویسندگان
چکیده
We show that the nth derivative of Riemann zeta function, when summed over non-trivial zeros zeta, is real and positive/negative in mean for n odd/even, respectively. this by giving a full asymptotic expansion these sums.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2022
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.03.004