On the roots of the equation ζ(s)=a
Given any complex number a , we prove that there are infinitely many simple roots of the equation ζ ( s ) = a with arbitrarily large imaginary part. Besides, we give a heuristic interpretation of a certain regularity of the graph of the curve t ↦ ζ ( 1 2 + i t ) . Moreover, we show that the curve R...
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| Veröffentlicht in: | Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2014-04, Vol.84 (1), p.1-15 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Given any complex number
a
, we prove that there are infinitely many simple roots of the equation
ζ
(
s
)
=
a
with arbitrarily large imaginary part. Besides, we give a heuristic interpretation of a certain regularity of the graph of the curve
t
↦
ζ
(
1
2
+
i
t
)
. Moreover, we show that the curve
R
∋
t
↦
(
ζ
(
1
2
+
i
t
)
,
ζ
′
(
1
2
+
i
t
)
)
is not dense in
C
2
. |
|---|---|
| ISSN: | 0025-5858 1865-8784 |
| DOI: | 10.1007/s12188-014-0093-7 |