Arithmetic properties of Euler series

DOI10.3103/S0027132215010088zbMath1330.11047MaRDI QIDQ493888

Vladimir G. Chirskii

Publication date: 4 September 2015

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

zbMATH Keywords

Euler series\(p\)-adic valuation

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Irrationality; linear independence over a field (11J72) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15) Approximation in non-Archimedean valuations (11J61)

Related Items (8)

On Padé approximations and global relations of some Euler-type series ⋮ ПЕРИОДИЧЕСКИЕ И НЕПЕРИОДИЧЕСКИЕ КОНЕЧНЫЕ ПОСЛЕДОВАТЕЛЬНОСТИ ⋮ ОЦЕНКА МНОГОЧЛЕНА ОТ ГЛОБАЛЬНО ТРАНСЦЕНДЕНТНОГО ПОЛИАДИЧЕСКОГО ЧИСЛА ⋮ Infinite algebraic independence of some almost polyadic numbers ⋮ Infinite linear independence of values of generalized hypergeometric series with irrational parameters at polyadic points ⋮ Explicit results for Euler’s factorial series in arithmetic progressions under GRH ⋮ Euler's factorial series and global relations ⋮ Euler's divergent series in arithmetic progressions

Cites Work

• Global relations
• Effective estimates for global relations on Euler-type series
• HERMITE-PADÉ APPROXIMANTS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS

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