Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables

DOI10.1007/s11139-017-9922-5zbMath1430.11123OpenAlexW2740718441MaRDI QIDQ681061

Masanori Katsurada, Takumi Noda

Publication date: 30 January 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-017-9922-5

zbMATH Keywords

asymptotic expansionEisenstein seriesMellin-Barnes integralJordan-Kronecker functionWeierstraß elliptic function

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items

Complete asymptotic expansions associated with various zeta-functions, Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Double zeta values, double Eisenstein series, and modular forms of level 2
• Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables
• Complete asymptotic expansions associated with Epstein zeta-functions
• Complete asymptotic expansions associated with Epstein zeta-functions. II
• On a conjecture for representations of integers as sums of squares and double shuffle relations
• FUNCTIONAL EQUATIONS FOR DOUBLE L-FUNCTIONS AND VALUES AT NON-POSITIVE INTEGERS
• Double shuffle relations of double zeta values and the double Eisenstein series at levelN
• On Generalized Lipschitz-type Formulae and Applications
• DIFFERENTIAL ACTIONS ON THE ASYMPTOTIC EXPANSIONS OF NON-HOLOMORPHIC EISENSTEIN SERIES
• Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
• On generalized Lipschitz-type formulae and applications II
• ON THE GENERALIZED TWO VARIABLE EISENSTEIN SERIES
• Analytic Continuation of the Series ∑(m + nz) -s