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超越数論セミナー

タイトル Irrationality and transcendence of alternating series via continued fractions
開催日時 2017年6月23日 ‎16:30―17:30
主催者
講演者 Jonathan Sondow 氏
場所 矢上キャンパス 14棟2階 ディスカッションルーム8
内容
 I give conditions for irrationality of the sum of an alternating series, and introduce a “simple” condition for its transcendence.
The proofs use continued fractions, irrationality measure, and the Thue-Siegel-Roth theorem on rational approximations to algebraic numbers.
The simple continued fractions for an infinite family of naturally-occurring transcendental numbers are given explicitly.
We also prove irrationality and transcendence for families of non-alternating series, using partial sums instead of continued fractions.
Mentioned along the way are Fermat, Fibonacci, and Liouville numbers, π, e, primorials, Sylvester’s sequence, an‎d some conjectures.
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