DIFFERENTIAL ACTIONS ON THE ASYMPTOTIC EXPANSIONS OF NON-HOLOMORPHIC EISENSTEIN SERIES

DOI10.1142/S1793042109002559zbMath1231.11049MaRDI QIDQ3644242

Masanori Katsurada, Takumi Noda

Publication date: 3 November 2009

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

asymptotic expansionMellin-Barnes integralnon-holomorphic Eisenstein serieseigenfunction equation

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Forms of half-integer weight; nonholomorphic modular forms (11F37) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Complete asymptotic expansions associated with various zeta-functions ⋮ Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables ⋮ Complete asymptotic expansions associated with Epstein zeta-functions. II ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers

Cites Work

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• Complete asymptotic expansions associated with Epstein zeta-functions
• Power series with the Riemann zeta-function in the coefficients
• A note on the non-holomorphic Eisenstein series
• Lectures on modular functions of one complex variable
• On an asymptotic formula of Ramanujan for a certain theta-type series
• Some identities for the Riemann zeta-function
• Elementary Dirichlet Series and Modular Forms
• Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
• Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
• On Epstein's Zeta Function (I)
• Modular Forms