Question

Proof of the Fundamental Theorem of Algebra: filling in some intermediate steps

score 481 · Answer 1 · 2020-07-01 23:43:45

481

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Proof of the Fundamental Theorem of Algebra: filling in some intermediate steps

Published on 01 Jul 2020 - 23:43

score 89 · Answer 2 · 2020-07-03 00:03:44

89

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$p(z)=1+z+\frac{z^2}{2}+...+\frac{z^m}{2^{m-1}}+3z^n$. How many zeroes does $p$ have counting multiplicities in the unit disk.

Published on 03 Jul 2020 - 0:03

score 638 · Answer 3 · 2020-07-04 12:22:16

638

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Non-constant holomorphic function on an annulus with constant modulus on boundary has at least two zeros on the annulus

Published on 04 Jul 2020 - 12:22

score 251 · Answer 4 · 2020-07-10 21:08:32

251

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Find the number of zeroes of $p(z)=z^6+z^3+10z^2+4z+3$ inside the annulus $1<|z|<2$

Published on 10 Jul 2020 - 21:08

score 42 · Answer 5 · 2020-07-20 21:59:35

42

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Bounding the roots of a complex polynomial of arbitrary degree

Published on 20 Jul 2020 - 21:59

score 65 · Answer 6 · 2023-01-30 22:05:38

65

Views

Find parameters $a,b,c \in\mathbb{R}$, such that following system is compatible

Published on 30 Jan 2023 - 22:05

score 25 · Answer 7 · 2023-02-28 19:00:04

25

Views

Missing detail FTA proof

Published on 28 Feb 2023 - 19:00

score 109 · Answer 8 · 2023-03-05 21:56:33

109

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An Alternate Formulation of Rouche's Theorem?

Published on 05 Mar 2023 - 21:56

score 99 · Answer 9 · 2023-04-02 15:32:42

99

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Conjecture, a monic polynomial with integer coefficients cannot have exactly one non-real root outside the open unit disk

Published on 02 Apr 2023 - 15:32

score 96 · Answer 10 · 2023-04-23 17:33:10

96

Views

Can we find a holomorphic function $f$ on an annulus such that $e^{f(z)}=z$

Published on 23 Apr 2023 - 17:33

score 39 · Answer 11 · 2023-05-12 08:14:07

39

Views

Sequence of functions uniform converges to f, then f is either zero or has no zeros, Rouche.

Published on 12 May 2023 - 8:14

score 21 · Answer 12 · 2023-06-22 12:37:51

Given entire functions $f,g$ having equal number of zeros in $D_r(0)$. Then exists an entire, non-vanishing $h$ st $|f - hg| < |f|$ on a large circle

score 98 · Answer 13 · 2023-11-09 15:37:45

98

Views

Rouche's Theorem Question, or not?

Published on 09 Nov 2023 - 15:37

score 222 · Answer 14 · 2023-11-22 14:08:03

222

Views

the zeros of a polynomial depend in a continuous way on its coefficients.

Published on 22 Nov 2023 - 14:08

score 114 · Answer 15 · 2023-11-28 21:47:11

114

Views

Roots of the polynomial $z^4+4z^3+6z^2-4z+4$ in the circle $|z+1|<1$.

Published on 28 Nov 2023 - 21:47

List Question

Proof of the Fundamental Theorem of Algebra: filling in some intermediate steps

$p(z)=1+z+\frac{z^2}{2}+...+\frac{z^m}{2^{m-1}}+3z^n$. How many zeroes does $p$ have counting multiplicities in the unit disk.

Non-constant holomorphic function on an annulus with constant modulus on boundary has at least two zeros on the annulus

Find the number of zeroes of $p(z)=z^6+z^3+10z^2+4z+3$ inside the annulus $1<|z|<2$

Bounding the roots of a complex polynomial of arbitrary degree

Find parameters $a,b,c \in\mathbb{R}$, such that following system is compatible

Missing detail FTA proof

An Alternate Formulation of Rouche's Theorem?

Conjecture, a monic polynomial with integer coefficients cannot have exactly one non-real root outside the open unit disk

Can we find a holomorphic function $f$ on an annulus such that $e^{f(z)}=z$

Sequence of functions uniform converges to f, then f is either zero or has no zeros, Rouche.

Given entire functions $f,g$ having equal number of zeros in $D_r(0)$. Then exists an entire, non-vanishing $h$ st $|f - hg| < |f|$ on a large circle

Rouche's Theorem Question, or not?

the zeros of a polynomial depend in a continuous way on its coefficients.

Roots of the polynomial $z^4+4z^3+6z^2-4z+4$ in the circle $|z+1|<1$.

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