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Results tagged with theta-series
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user 70925
2
votes
0
answers
101
views
Generalised theta series for fixed-rank sublattices
The theta series for a lattice $\Lambda$ is defined by
$$\displaystyle \Theta_\Lambda(q) = \sum_{x \in \Lambda} q^{x \cdot x}.$$
Setting $q=e^{-\pi\tau}$ yields the (maybe more usual) related theta se …
- 313
4
votes
1
answer
288
views
Closed formula for reversion of Jacobi theta series
Considering the Jacobi theta: $\theta_3(z) = \sum_{n\in\mathbb{Z}} q^{n^2}$,
we can invert $\theta_3-1$ in a small enough neighbourhood of 0.
Routine computation with Lagrange-Burmann inversion gives …
- 313