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Multiplicity one theorems for Fourier-Jacobi models
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abstract
For every genuine irreducible admissible smooth representation $\pi$ of the metaplectic group $\widetilde{\Sp}(2n)$ over a p-adic field, and every smooth oscillator representation $\omega_\psi$ of $\widetilde{\Sp}(2n)$, we prove that the tensor product $\pi\otimes \omega_\psi$ is multiplicity free as a smooth representation of the symplectic group $\Sp(2n)$. Similar results are proved for general linear groups and unitary groups.
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Squarefree numbers in short intervals: explicit and formalized
For intervals of length H = X^{1/5 - 2/90935 + ε}, the number of squarefree integers differs from (6/π²)H by at most an explicit constant times H X^{-ε/10^{25}}.
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