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An algebraic independence result for Euler products of finite degree
Author(s):
Alexandru
Zaharescu;
Mohammad
Zaki
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1275-1283.
MSC (2000):
Primary 11J85, 13J99
Posted:
October 9, 2008
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Abstract:
We investigate the algebraic independence of some derivatives of certain multiplicative arithmetical functions over the field of complex numbers.
References:
-
- 1.
- E. Alkan, A. Zaharescu, M. Zaki, Arithmetical functions in several variables, Int. J. Number Theory 1 (2005), no. 3, 383-399. MR 2175098 (2006k:11008)
- 2.
- E. Alkan, A. Zaharescu, M. Zaki, Multidimentional averages and Dirichlet convolution, Manuscripta Math. 123 (2007), 251-267. MR 2314084 (2008d:11089)
- 3.
- B. Berndt, K. Ono, Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary, Sém. Lothar. Combin. 42 (1999). MR 1701582 (2000i:01027)
- 4.
- E.D. Cashwell, C.J. Everett, The ring of number-theoretic functions, Pacific J. Math. 9 (1959), 975-985. MR 0108510 (21:7226)
- 5.
- W. Narkiewicz, On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81-94. MR 0159778 (28:2994)
- 6.
- W. Narkiewicz, Some unsolved problems, Colloque de Théorie des Nombres (Univ. Bordeaux, Bordeaux, 1969), pp. 159-164. Bull. Soc. Math. France, Mem. No. 25, Soc. Math. France, Paris, 1971. MR 0466060 (57:5943)
- 7.
- K. Ono, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and
-series, CBMS Regional Conference Series in Mathematics 102. Published for the Conference Board of the Mathematical Sciences, Washington, DC, by the American Mathematical Society, Providence, RI, 2004. MR 2020489 (2005c:11053) - 8.
- S. Ramanujan, Collected Papers, Chelsea, New York, 1962.
- 9.
- A. Schinzel, A property of the unitary convolution, Colloq. Math. 78 (1998), no. 1, 93-96. MR 1658143 (99k:11010)
- 10.
- E. D. Schwab, Möbius categories as reduced standard division categories of combinatorial inverse monoids, Semigroup Forum 69 (2004), no. 1, 30-40. MR 2063975 (2005b:20121a)
- 11.
- E. D. Schwab, The Möbius category of some combinatorial inverse semigroups, Semigroup Forum 69 (2004), no. 1, 41-50. MR 2063976 (2005b:20121b)
- 12.
- E. D. Schwab, G. Silberberg, A note on some discrete valuation rings of arithmetical functions, Arch. Math. (Brno) 36 (2000), 103-109. MR 1761615 (2001d:13022)
- 13.
- E. D. Schwab, G. Silberberg, The valuated ring of the arithmetical functions as a power series ring, Arch. Math. (Brno) 37 (2001), 77-80. MR 1822767
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Additional Information:
Alexandru
Zaharescu
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email:
zaharesc@math.uiuc.edu
Mohammad
Zaki
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email:
mzaki@math.uiuc.edu
DOI:
10.1090/S0002-9939-08-09622-6
PII:
S 0002-9939(08)09622-6
Keywords:
Arithmetical functions,
algebraic independence
Received by editor(s):
January 25, 2008,
Received by editor(s) in revised form:
May 1, 2008
Posted:
October 9, 2008
Communicated by:
Ken Ono
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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