TY - JOUR
T1 - A HARMONIC SUM over NONTRIVIAL ZEROS of the RIEMANN ZETA-FUNCTION
AU - Brent, Richard P.
AU - Platt, David J.
AU - Trudgian, Timothy S.
N1 - Publisher Copyright:
© 2020 Australian Mathematical Publishing Association Inc..
PY - 2021/8
Y1 - 2021/8
N2 - We consider the sum, where ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in an interval, and examine its behaviour as. We show that, after subtracting a smooth approximation the sum tends to a limit, which can be expressed as an integral. We calculate H to high accuracy, using a method which has error. Our results improve on earlier results by Hassani ['Explicit approximation of the sums over the imaginary part of the non-trivial zeros of the Riemann zeta function', Appl. Math. E-Notes 16 (2016), 109-116] and other authors.
AB - We consider the sum, where ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in an interval, and examine its behaviour as. We show that, after subtracting a smooth approximation the sum tends to a limit, which can be expressed as an integral. We calculate H to high accuracy, using a method which has error. Our results improve on earlier results by Hassani ['Explicit approximation of the sums over the imaginary part of the non-trivial zeros of the Riemann zeta function', Appl. Math. E-Notes 16 (2016), 109-116] and other authors.
KW - Riemann zeta-function
KW - acceleration
KW - nontrivial zeros
UR - http://www.scopus.com/inward/record.url?scp=85096680798&partnerID=8YFLogxK
U2 - 10.1017/S0004972720001252
DO - 10.1017/S0004972720001252
M3 - Article
SN - 0004-9727
VL - 104
SP - 59
EP - 65
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 1
ER -