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April 2009
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13 Reads
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1 Citation
Computational Methods and Function Theory
We investigate the following problem: given a positive integer n, which are the smallest values of the constants s n, such that the zeros of f _{a,n}(z) := \matrix{\sum^n_{k=0}} z^k/a^{k^2} are with negative real parts when a > s n?
6 Reads
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1 Citation
A real polynomial is called Hurwitz (stable) if all its zeros have negative real parts. For a given n 2 N we find the smallest pos- sible constant dn > 0 such that if the coecients of
... Moreover, as shown by Nguyen and Vishnyakova [112], the partial theta function is extremal in the sense that any entire function of the form f (x) = n 0 a n x n (a n > 0) for which the sequence a 2 n /(a n−1 a n+1 ) is decreasing with limit lim n→∞ a 2 n /(a n−1 a n+1 ) = b q ∞ is in the Laguerre-Pólya class. In a similar vein, Katkova and Vishnyakova [72] have proven the existence of a constant, s ∞ , such that all roots of Θ p (x; q) have negative real parts if 1/q < s ∞ . ...
Reference:
Partial theta functions
April 2009
Computational Methods and Function Theory
... is not Hurwitz stable( [14]). ...
