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A note on the trace formula
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In this mostly expository note, we prove explicit formulas for the traces of Hecke operators on spaces of cusp forms fixed by Atkin-Lehner involutions, which are suitable for efficient implementation. In addition, we correct a couple of errors in previously published formulas.
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Cited by 1 Pith paper
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Joint level-weight murmurations: prime averaging and the cubic pointwise range
Unconditionally, joint averages of root-number-weighted prime traces of squarefree-level holomorphic newforms converge to an explicit atomic measure on rational squares for every K = X^ρ with 0 < ρ < 1.
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