arXiv subjects

Brandon Williams

Publications and source records attributed to Brandon Williams.

39 records · Page 3Linked to original sources

arXiv2017

Vector-valued Eisenstein series of small weight

We study the (mock) Eisenstein series $E_k$ of weight $k \in \{1,3/2,2\}$ for the Weil representation on an even lattice, defined as the result of Bruinier and Kuss's coefficient formula for the Eisenstein series naively evaluated at $k$. We describe the transformation law of $E_k$ in general. Most of this note is dedicated to collecting examples where the coefficients of $E_k$ contain interesting arithmetic information. Finally we make a few remarks about the case $k=1/2$.

math.NT↗

arXiv2017

Poincaré square series of small weight

We extend the author's earlier computation and give coefficient formulas for the (quasimodular) Poincaré square series of weight 3/2 and weight 2 for the dual Weil representation for an even lattice.

math.NT↗

arXiv2017

Poincaré square series for the Weil representation

We calculate the Jacobi Eisenstein series of weight $k \ge 3$ for a certain representation of the Jacobi group, and evaluate these at $z = 0$ to give coefficient formulas for a family of modular forms $Q_{k,m,β}$ of weight $k \ge 5/2$ for the (dual) Weil representation on an even lattice. The forms we construct always contain all cusp forms within their span. We explain how to compute the representation numbers in the coefficient formulas for $Q_{k,m,β}$ and the Eisenstein series of Bruinier and Kuss $p$-adically to get an efficient algorithm. The main application is in constructing automorphic products.

math.NT↗