대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권4호
  • /
  • Pages.695-708
  • /
  • 2005
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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OBSERVATIONS ABOUT ALGEBRAIC DEPENDENCE OF DIRICHLET SERIES

  • 발행 : 2005.07.01
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초록

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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참고문헌

  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