Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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OBSERVATIONS ABOUT ALGEBRAIC DEPENDENCE OF DIRICHLET SERIES

  • Published : 2005.07.01
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Abstract

Certain observations about formal Dirichlet series whose coefficients are arithmetic functions are made. These include for example algebraic independence and representation as infinite series of logarithms.

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References

  1. E. D. Cashwell and C. J. Everett, The ring of number-theoretic functions, Pacific J. Math. 9 (1959), 975-985
  2. E. D. Cashwell and C. J. Everett, Formal power series, Pacific J. Math. 13 (1963), 45-641
  3. C. A. Charalambides, Enumerative Combinatorics, Chapman & Hall, Boca Raton, 2002
  4. A. Ostrowski, Uber Dirichletsche Reihen und algebraische differentialgleichungen, Math. Z. 8 (1920), 241-298 https://doi.org/10.1007/BF01206530
  5. H. N. Shapiro and G. H. Sparer, On algebraic independence of Dirichlet series, Comm. Pure Appl. Math. 39 (1986), 695-745 https://doi.org/10.1002/cpa.3160390602