Kronecker limit formulas for parabolic, hyperbolic and elliptic Eisenstein series via Borcherds products

Nonholomorphic Eisenstein series, the Kronecker limit formula, and the hyperbolic Laplacian

Convolution Dirichlet Series and a Kronecker Limit Formula for Second-order Eisenstein Series

In this article we derive analytic and Fourier aspects of a Kronecker limit formula for second-order Eisenstein series. Let Γ be any Fuchsian group of the first kind which acts on the hyperbolic upper half-space H such that the quotient Γ\H has finite volume yet is non-compact. Associated to each cusp of Γ\H, there is a classically studied first-order non-holomorphic Eisenstein series E(s, z) w...

p-ADIC EISENSTEIN-KRONECKER FUNCTIONS AND THE ELLIPTIC POLYLOGARITHM FOR CM ELLIPTIC CURVES

In this paper, we construct p-adic analogues of the Kronecker double series, which we call the Eisenstein-Kronecker series, as Coleman functions on an elliptic curve with complex multiplication. We then show that the periods of the specialization of the p-adic elliptic polylogarithm sheaf to arbitrary non-zero points of the elliptic curve may be expressed using these functions.

Borcherds Products Associated with Certain Thompson Series

Let M ! 1/2 be the additive group consisting of nearly holomorphic modular forms of weight 1/2 for Γ0(4) whose Fourier coefficients are integers and satisfy the Kohnen’s “plus space” condition (i.e. n-th coefficients vanish unless n ≡ 0 or 1 modulo 4). We also let B be the multiplicative group consisting of meromorphic modular forms for some characters of SL2(Z) of integral weight with leading ...

Unimodality via Kronecker Products

We present new proofs and generalizations of unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of representations of Sn. Other applications of this approach include strict unimodality of the diagonal q-binomial coefficients and unimodality of certa...