Abstract
In 1919 Ramanujan conjectured congruences for certain classes of ordinary partitions modulo powers of 5 and 7 which were later proved by G.N. Watson. The corresponding congruences for colored generalized Frobenius partitions with 5 and 7 colors were recently derived by establishing a relationship between these partitions and ordinary partitions [5]. In this paper we prove similar congruences for colored generalized Frobenius partitions with 3 colors modulo powers of 3 using certain generating function identities and the modular equation of order 3.
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References
George E. Andrews, “Generalized Frobenius Partitions” Memoirs of the American Mathematical Society, Volume 301, Providence, RI, May 1984.
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Louis W. Kolitsch, A Relationship between Certain Colored General-ized Frobenius Partitions and Ordinary Partitions, Journal of Number Theory 33 (1989), 220–223.
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Dedicated to Paul Bateman
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© 1990 Birkhäuser Boston
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Kolitsch, L.W. (1990). A Congruence for Generalized Frobenius Partitions with 3 Colors Modulo Powers of 3. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_21
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DOI: https://doi.org/10.1007/978-1-4612-3464-7_21
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3481-0
Online ISBN: 978-1-4612-3464-7
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