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Regular trace formula and base change lifting. (English) Zbl 0666.10020

A trace formula for regular test function is called here a regular trace formula. Such a formula is established here for \(\mathrm{GL}(2)\) and is applied to prove the cyclic base change theory for \(\mathrm{GL}(2)\).

MSC:

11F72 Spectral theory; trace formulas (e.g., that of Selberg)
22E50 Representations of Lie and linear algebraic groups over local fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
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