The classical absolute-value conjecture for Xi zeroes

Let Ξ(χ,t)=Λ(χ,1/2+it)\Xi(\chi,t)=\Lambda(\chi,1/2+it) for an abelian character χ\chi over a number field. The classical absolute-value conjecture. For every e0e\geq0, there are at most two zeroes of Ξ(χ,t)\Xi(\chi,t), counted without multiplicity, having absolute value ee.

This is presented as the direct classical analogue of the characteristic-pp reciprocal-zero conjecture. The bound of two reflects the functional equation sending tt to t-t, while the conjecture remains unproved.

Sources & referencesView supporting material

Primary source

David Goss, “A Riemann Hypothesis for characteristic p L-functions”, arXiv:math/9907019 (1999).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.