# セミナー

## 超越数論セミナー

タイトル Irrationality and transcendence of alternating series via continued fractions 2017年6月23日 ‎16:30―17:30 Jonathan Sondow 氏 矢上キャンパス 14棟2階　ディスカッションルーム8 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.