Eisenstein Series and Partition Functions
Copyright policy )Eisenstein Series and Partition Functions
ABSTRACTIn this work, using quotients of Dedekind eta functions of weight , we express certain Eisenstein series associated with congruence subgroups , of arbitrary weight. We then obtain new Ramanujan type identities on partition functions associated with certain eta quotients. The method we apply in this work is inspired by the work of Fine, Kolberg, and Garvan on Eisenstein series. It is different from those used by Ramanujan, Zuckerman, Carlitz, and others.
- Centre d’Economie Industrielle - CERNA France
- Laboratoire de Mathématiques et Modélisation d'Evry France
- Jeonbuk National University Korea (Republic of)
Other character sums and Gauss sums, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), eta quotients, Eisenstein series, modular functions, Partition identities; identities of Rogers-Ramanujan type, Dedekind eta function, Dedekind sums, eta function, \(L\)-function, Legendre symbols, hauptmodul, divisors functions, partition functions
Other character sums and Gauss sums, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), eta quotients, Eisenstein series, modular functions, Partition identities; identities of Rogers-Ramanujan type, Dedekind eta function, Dedekind sums, eta function, \(L\)-function, Legendre symbols, hauptmodul, divisors functions, partition functions
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