This extended abstract provides an overview of the results presented in [8, 9] regarding the large-coalition asymptotics of collusion-resistant fingerprinting and the asymptotics of group testing for large numbers of defectives.

The heat trace asymptotics are discussed for operators of Laplace type with Dirichlet, Robin, spectral, D/N, and transmittal boundary conditions. The heat content asymptotics are discussed for operators with time dependent coefficients and Dirichlet or Robin boundary conditions.

We study the asymptotics of Hankel determinants constructed using the values ζ(an + b) of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.

We describe the heat kernel asymptotics for roots of a Laplace type operator ∆ on a closed manifold. A previously known relation between the Wodzicki residue of ∆ and heat trace asymptotics is shown to hold pointwise for the corresponding densities.

New limit theory is developed for co-moving systems with explosive processes, connecting continuous and discrete time formulations. The theory uses double asymptotics with infill (as the sampling interval tends to zero) and large time span asymptotics. The limit theory explicitly involves initial conditions, allows for drift in the system, is provided for single and multiple explosive regressor...

The initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve L-function at s = 1. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the L-function and that the constant in the asymptotics has an unexpected factor of √ 2. We extend Goldfeld’s theorem to an analysis of partial Euler products for ...

BASED on the channel coding theorem, there exists a sequence of codes for the given channel W such that the average error probability goes to 0 when the transmission rate R is less than CW . That is, if the number n of applications of the channel W is sufficiently large, the average error probability of a good code goes to 0. In order to evaluate the average error probability with finite n, we ...

A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler’s generating function ∏∞ k=1 S(z k) for partitions, where S(z) = (1 − z)−1. By applying a method due to Khintchine, we extend Meinardus’ theorem to find the asymptotics...