An analog of the prime number theorem for finite fields via truncated polylogarithm expansions

DOI10.1090/mcom/3247zbMath1377.05011OpenAlexW2566607440MaRDI QIDQ4600713

Stephen W. Neville, Niko Rebenich, Ulrich Speidel, T. Aaron Gulliver

Publication date: 12 January 2018

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3247

zbMATH Keywords

polylogarithmdivergent seriesirreducible polynomialsEulerian polynomialsLerch transcendentaperiodic necklaces.prime polynomial counting functionsuperasymptotic expansion

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Polynomials over finite fields (11T06) Asymptotic enumeration (05A16) Polylogarithms and relations with (K)-theory (11G55) Hurwitz and Lerch zeta functions (11M35) Analytic computations (11Y35)

Cites Work

• The Lerch zeta function. III: Polylogarithms and special values
• Ein Analogon zum Primzahlsatz für algebraische Funktionenkörper. (An analog of the prime number theorem for algebraic function fields)
• Witt vectors and the algebra of necklaces
• Revisiting Gauss's analogue of the prime number theorem for polynomials over a finite field
• The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
• A probabilistic interpretation of Eulerian numbers
• Subgroup growth.
• Asymptotic expansions of the Hurwitz--Lerch zeta function
• On a function which occurs in the theory of the structure of polymers
• Counting irreducible polynomials over finite fields
• Eulerian Polynomials: From Euler’s Time to the Present
• Algebraic Function Fields and Codes
• Obtaining Specified Irreducible Polynomials over Finite Fields
• Permutations and sequences with repetitions by number of increases
• Eulerian number asymptotics
• Eulerian Numbers
• Asymptotic properties of eulerian numbers
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