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Results tagged with zeroes
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user 59219
9
votes
1
answer
404
views
Existence of Laurent series with zeroes at $e^{2n}$ ($n \in \Bbb{N}_0$) and extremely fast c...
Real and Complex Analysis, Theorem 15.20]) which shows that if $f : \Bbb{C} \to \Bbb{C}$ is holomorphic, then
$$
M(2r) \geq \prod_{n=1}^{n(2r)} \frac{2r}{|\alpha_n|},
$$
where the $\alpha_i$ are the zeroes … of $f$, and where $|\alpha_1| \leq |\alpha_2| \leq \dots$, and where $n(2r)$ is the number of zeroes of $f$ satisfying $|z| < 2r$. …
- 734
5
votes
1
answer
168
views
Existence of Laurent series with zeroes at $𝑒^{2𝑛}$ ($𝑛∈ℕ_0$) and even faster coefficient...
This is an extension of an earlier question of mine which corresponds to the case $A = 1$. Precisely, my question is as follows:
Given $A > 0$ fixed but arbitrary, is there a non-trivial sequence $(c …
- 734