On some partition functions related to some mock theta function

• Autorzy: Patkowski A. E.
• Języki publikacji: EN

Abstrakty

EN

We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.

Słowa kluczowe

EN

q-series; partitions; mock theta functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 1
• Strony: 1--8
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Patkowski A. E.

• Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, U.S.A.,

Bibliografia

• [1] G. E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc. 293 (1986), 113-134.
• [2] G. E. Andrews, F. J. Dyson and D. Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), 391-407.
• [3] G. E. Andrews, J. Jiménez-Urroz and K. Ono, q-series identities and values of certain L-functions, Duke Math. J. 108 (2001), 395-419.
• [4] W. N. Bailey, Identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 50 (1949), 1-10.
• [5] N. J. Fine, Basic Hypergeometric Series and Applications, Math. Surveys Monogr. 27, Amer. Math. Soc., Providence, RI, 1988.
• [6] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, 1990.