A curious identity for Bernoulli numbers
We prove a curious identity for the Bernoulli numbers.
math.NT↗
arXiv subjects
Daniel B. Grunberg
Publications and source records attributed to Daniel B. Grunberg.
Sequences of enumerative geometry: congruences and asymptotics
We study the integer sequence v_n of numbers of lines in hypersurfaces of degree 2n-3 of P^n, n>1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the v_n are described (in an appendix by Don Zagier). An attempt is made at a similar analysis of two other enumerative sequences: the number of rational plane curves and the number of instantons in the quintic threefold.
math.NT↗
N=4 Characters in Gepner Models, Orbits and Elliptic Genera
We review the properties of characters of the N=4 SCA in the context of a non-linear sigma model on $K3$, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same expression for the $K3$ elliptic genus using three different Gepner models ($1^6$, $2^4$ and $4^3$ theories), detailing the orbits and verifying that their coefficients $F_i$ are given by elementary modular functions. We also reveal the orbits for the $1^3 2^2$, $1^4 4$ and $1^2 4^2$ theories. We derive relations for cubes of theta functions and study the function $ {1\overη} \sum_{n\in \Z} (-1)^n (6n+1)^k q^{(6n+1)^2 /24} $ for $k=1,2,3,4$.
hep-th↗