Euler's divergent series in arithmetic progressions

zbMath1443.11138arXiv1809.03859MaRDI QIDQ3120417

Tapani Matala-aho, Louna Seppälä, Anne-Maria Ernvall-Hytönen

Publication date: 4 March 2019

Full work available at URL: https://arxiv.org/abs/1809.03859

zbMATH Keywords

divergent series\(p\)-adic numberglobal relation

Mathematics Subject Classification ID

Approximation in non-Archimedean valuations (11J61)

Related Items (8)

Arithmetic properties of the values of generalized hypergeometric series with polyadic transcendental parameters ⋮ Transcendence of \(p\)-adic values of generalized hypergeometric series with transcendental polyadic parameters ⋮ Arithmetic properties of values at polyadic Liouville points of Euler-type series with polyadic Liouville parameter ⋮ Infinite linear independence with constraints on a subset of prime numbers for values of Euler-type series with polyadic Liouville parameter ⋮ Explicit results for Euler’s factorial series in arithmetic progressions under GRH ⋮ New problems in the theory of transcendental polyadic numbers ⋮ Euler's factorial series at algebraic integer points ⋮ Euler's factorial series, Hardy integral, and continued fractions

Cites Work

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• Arithmetic properties of Euler series
• Explicit bounds for primes in arithmetic progressions
• On algebraic relations in non-archimedean fields
• Euler's factorial series and global relations
• Rational approximations of the exponential function at rational points
• Effective estimates for global relations on Euler-type series
• On the arithmetic properties of generalized hypergeometric series with irrational parameters
• Arithmetic properties of polyadic series with periodic coefficients

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