On the Phragmén-Lindelöf principle
نویسندگان
چکیده
منابع مشابه
The algebraic surfaces on which the classical Phragmén - Lindelöf theorem holds
Let V be an algebraic variety in Cn . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by |z| + o(|z|) on V and by 0 on the real points in V already is bounded by A| Im z|. For algebraic ...
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ζ(0 + it) = O(|t| 1 2 + ), for each > 0. Apply the Phragmén–Lindelöf Theorem to ζ(s) in a small interval containing 1. Clearly, we can make the linear function arising from the Phragmén–Lindelöf Theorem to pass arbitrarily close to 0 at σ = 1. Thus, as |t| → ∞, ζ(1 + it) = O(|t| ), for each > 0. To apply the Phragmén–Lindelöf Theorem to ζ(s) in the strip 0 ≤ σ ≤ 1, we set k(σ) = aσ + b. Thus, k...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1946
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1946-0019117-0