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The Whittaker period formula on Metaplectic SL(2)
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abstract
The Whittaker period formula on metaplectic $SL(2)$ was previously established only when the base field $F$ is totally real. We present a new simple proof that works for all base number fields. Our local argument is uniform at every local place of $F$, based on the isometry property of quadratic Fourier transform and the estimates of matrix coefficients and Whittaker functions imposed by the unitariness of the local representations.
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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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