The classical absolute-value conjecture for Xi zeroes
The classical absolute-value conjecture for Xi zeroes
Let for an abelian character over a number field. The classical absolute-value conjecture. For every , there are at most two zeroes of , counted without multiplicity, having absolute value .
This is presented as the direct classical analogue of the characteristic- reciprocal-zero conjecture. The bound of two reflects the functional equation sending to , while the conjecture remains unproved.
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Primary source
David Goss, “A Riemann Hypothesis for characteristic p L-functions”, arXiv:math/9907019 (1999).
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