Diophantine properties of numbers related to Catalan's constant | Zendy

Tanguy Rivoal | Zendy; Wadim Zudilin | Zendy

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Diophantine properties of numbers related to Catalan's constant

Author(s) -

Tanguy Rivoal,

Wadim Zudilin

Publication year - 2003

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/s00208-003-0420-2

Subject(s) - mathematics , diophantine equation , sketch , lemma (botany) , catalan number , parity (physics) , constant (computer programming) , series (stratigraphy) , diophantine set , catalan , combinatorics , discrete mathematics , pure mathematics , physics , computer science , algorithm , philosophy , humanities , programming language , ecology , paleontology , poaceae , particle physics , biology

This article deals with Dirichlet’s beta function. Using the recursion (37), we have verified numerically (up to n = 1000) that 16ⁿ ·un ∊ℤand d²₂n · 16ⁿ · vn ∊ℤ: this is more that one can get from Lemma 6, although it is not sufficient to prove the irrationality of Catalan’s constant

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