Central values of twisted base change L-functions associated to Hilbert modular forms

Pi, Qinghua

doi:10.1016/j.jnt.2018.03.005

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“…Recently, Pi [Pi18] proved a certain stable average formula similar to that of [FW09], which allows for squares and cubes dividing the level. More precisely, Pi averages over representations which are fixed depth 0 or simple supercuspidals π v at a given set of places.…”

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confidence: 99%

Exact double averages of twisted L-values

Martin¹

2020

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Consider central L-values of even weight elliptic or Hilbert modular forms f twisted by ideal class characters χ of an imaginary quadratic extension K. Fixing χ, and assuming K is inert at each prime dividing the level, one knows simple exact formulas for averages over newforms f of squarefree levels satisfying a parity condition on the number of prime factors. These averages stabilize when the level is large with respect to K (the "stable range").In weight 2, we obtain exact formulas for a simultaneous average over both f and χ. We allow for non-squarefree levels with any number of prime factors, and ramification or splitting of K above the level. Under elementary conditions on the level, these double averages are "stable" in all ranges. Two consequences are generalizations of the aforementioned stable (single) averages and effective results on nonvanishing of central L-values.

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confidence: 99%