On the Behavior of Power Series with Completely Additive Coefficients
Oleg Petrushov
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015), p. 217-225 / Harvested from The Polish Digital Mathematics Library
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Consider the power series (z)=∑n=1∞α(n)zⁿ, where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity e2πil/q. We give effective omega-estimates for (e(l/pk)r) when r → 1-. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:281243 
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     title = {On the Behavior of Power Series with Completely Additive Coefficients},
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     language = {en},
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Oleg Petrushov. On the Behavior of Power Series with Completely Additive Coefficients. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 217-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba8018-1-2016/