Quantization and Arithmetic pp 117-141 | Cite as

# Back to the Weyl Calculus

Chapter

## Abstract

We come back to the constructions of Section 3: our standing assumption in this chapter is that the number again a Γ-invariant distribution. Recall that ? is the set of squares in (ℤ/

*N*is 4 times a squarefree odd integer, but it does not have to coincide with 4 or 12 any more. Then, not every element of (ℤ/*N*ℤ)^{×}is a square, and we have to consider the full set of distributions ϖ_{ρ}as defined in Lemma 3.2: we introduce the linear combination$$
W_N \left( {x,\xi } \right) = \sum\limits_{\rho \in R_N } {W\left( {\varpi _\rho ,\varpi _\rho } \right)\left( {x,\xi } \right)} ,
$$

*N*ℤ)^{×}and that*R*_{ N }is a set of representatives of (ℤ/*N*ℤ)^{×}mod Λ.## Keywords

Wigner Function Prime Divisor Fundamental Domain Dirichlet Series Integral Kernel
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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