New representations of Ramanujan's tau function

Author:
John A. Ewell

Journal:
Proc. Amer. Math. Soc. **128** (2000), 723-726

MSC (1991):
Primary 11A25; Secondary 11B75

DOI:
https://doi.org/10.1090/S0002-9939-99-05289-2

Published electronically:
July 28, 1999

MathSciNet review:
1657735

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Abstract | References | Similar Articles | Additional Information

Abstract: Several formulas for Ramanujan's function , defined by

are presented. We also present a congruence modulo 3 for some of the function values.

**1.**J. A. Ewell,*Arithmetical consequences of a sextuple product identity*, Rocky Mountain J. of Math., v. 25 (1995), 1287-1293. MR**97e:11129****2.**J. A. Ewell,*A note on a Jacobian identity*, Proc. Amer. Math. Soc., v. 126 (1998), 421-423. MR**98k:33030****3.**G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Fourth edition, Clarendon Press, Oxford, 1960.**4.**C.J. Moreno,*A necessary and sufficient condition for the Riemann hypothesis for**Ramanujan's zeta function*, Illinois J. of Math., v. 18 (1974), 107-114. MR**48:8410****5.**S. Ramanujan,*Collected papers*, Chelsea, New York, 1962.**6.**R. Sivaramakrishnan,*Classical theory of arithmetic functions*, Dekker, New York, 1989. MR**90a:11001**

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Additional Information

**John A. Ewell**

Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115

DOI:
https://doi.org/10.1090/S0002-9939-99-05289-2

Keywords:
Ramanujan's tau function

Received by editor(s):
May 13, 1998

Published electronically:
July 28, 1999

Communicated by:
Dennis A. Hejhal

Article copyright:
© Copyright 1999
American Mathematical Society