论文标题
一类广义全体形态Eisenstein系列的渐近扩展，Ramanujan的$ζ公式（2k+1）$，Weierstrass的椭圆形和相关功能
Asymptotic expansions for a class of generalized holomorphic Eisenstein series, Ramanujan's formula for $ζ(2k+1)$, Weierstrass' elliptic and allied functions
论文作者
论文摘要
For a class of generalized holomorphic Eisenstein series, we establish complete asymptotic expansions (Theorems~1~and~2), which together with the explicit expression of the latter remainder (Theorem~3), naturally transfer to several new variants of the celebrated formulae of Euler and of Ramanujan for specific values of the Riemann zeta-function (Theorem~4 and衡量的〜4.1--4.5），以及各种整数重量（推论〜4.6）的经典Eisenstein系列的各种模块化关系，以及Weierstraß的椭圆形和相关功能（推论〜4.7---4.9）。证明中的至关重要的r {p。
For a class of generalized holomorphic Eisenstein series, we establish complete asymptotic expansions (Theorems~1~and~2), which together with the explicit expression of the latter remainder (Theorem~3), naturally transfer to several new variants of the celebrated formulae of Euler and of Ramanujan for specific values of the Riemann zeta-function (Theorem~4 and Corollaries~4.1--4.5), and to various modular type relations for the classical Eisenstein series of any even integer weight (Corollary~4.6) as well as for Weierstraß' elliptic and allied functions (Corollaries~4.7--4.9). Crucial r{ô}les in the proofs are played by certain Mellin-Barnes type integrals, which are manipulated with several properties of confluent hypergeometric functions.
