Gross's Euler–Poincaré orbital-integral conjecture
Gross's Euler–Poincaré orbital-integral conjecture
Let be a non-Archimedean local field, let be the reductive group under consideration, and let be the Euler–Poincaré function with respect to a Haar measure on . For a semisimple element with centralizer , write for its orbital integral, let be any Haar measure on , and let be the Euler–Poincaré measure on . Gross's Euler–Poincaré conjecture.
The conjecture identifies the orbital integrals of the Euler–Poincaré function with Euler–Poincaré measures precisely on elliptic semisimple classes. It is attributed here to Gross; the supplied text does not state whether it has been resolved.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Takuro Fukayama, “The number of cuspidal representations over a function field and its behavior under base changes”, arXiv:2504.20564 (2025).
Additional references
2 papers in this index state this conjecture (2022–2025). The statement above is taken from the most recent of them; the others are arXiv:2208.01069.
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