TY - JOUR
T1 - On the zeros of linear combinations of derivatives of the Riemann zeta function
AU - Paolina Koutsaki, K.
AU - Tamazyan, Albert
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - In this paper, the zeros of linear combinations of the Riemann zeta function and its derivatives are studied. We establish an asymptotic formula for the number of zeros in a rectangle of height T. We also find a sharp asymptotic formula for the supremum of the real parts of zeros of such combinations in a certain family.
AB - In this paper, the zeros of linear combinations of the Riemann zeta function and its derivatives are studied. We establish an asymptotic formula for the number of zeros in a rectangle of height T. We also find a sharp asymptotic formula for the supremum of the real parts of zeros of such combinations in a certain family.
KW - Riemann zeta function
KW - linear combination of derivatives
KW - non-real zeros
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U2 - 10.1142/S1793042116501049
DO - 10.1142/S1793042116501049
M3 - Article
AN - SCOPUS:84955056118
VL - 12
SP - 1703
EP - 1723
JO - International Journal of Number Theory
JF - International Journal of Number Theory
SN - 1793-0421
IS - 6
ER -