Research output: Contribution to journal › Article › peer-review
On zeroes and poles of Helson zeta functions. / Bochkov, I.; Romanov, R.
In: Journal of Functional Analysis, Vol. 282, No. 8, 109398, 15.04.2022.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On zeroes and poles of Helson zeta functions
AU - Bochkov, I.
AU - Romanov, R.
N1 - Publisher Copyright: © 2022 Elsevier Inc.
PY - 2022/4/15
Y1 - 2022/4/15
N2 - We show that the analytic continuations of Helson zeta functions ζχ(s)=∑1∞χ(n)n−s can have essentially arbitrary poles and zeroes in the strip 21/40<ℜs<1 (unconditionally), and in the whole critical strip 1/2<ℜs<1 under Riemann Hypothesis.
AB - We show that the analytic continuations of Helson zeta functions ζχ(s)=∑1∞χ(n)n−s can have essentially arbitrary poles and zeroes in the strip 21/40<ℜs<1 (unconditionally), and in the whole critical strip 1/2<ℜs<1 under Riemann Hypothesis.
KW - Dirichlet series
KW - Helson zeta function
KW - Meromorphic extension
UR - http://www.scopus.com/inward/record.url?scp=85123749328&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/5b7be008-7100-3ec2-be6d-adc0cb4536f3/
U2 - 10.1016/j.jfa.2022.109398
DO - 10.1016/j.jfa.2022.109398
M3 - Article
AN - SCOPUS:85123749328
VL - 282
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 8
M1 - 109398
ER -
ID: 98050016