The Euler-factor conjecture for Calabi–Yau differential operators

Less than 1 year old · traced to

Let L\mathcal{L} be a Calabi–Yau operator arising as a Picard–Fuchs operator for a Calabi–Yau motive XφX_\varphi. Let p≥5p\geq5, and let φ\varphi be such that D(Teich⁡(φ))−1D(\operatorname{Teich}(\varphi))^{-1} is defined in Qp\mathbb{Q}_p and ord⁡p(D(Teich⁡(φ)))≤0\operatorname{ord}_p(D(\operatorname{Teich}(\varphi)))\leq0. For sufficiently large M(L,p)M(\mathcal{L},p), the Euler-factor conjecture. The Euler factor Ep(b−1)(Xφ,T)E_p^{(b-1)}(X_\varphi,T) equals the polynomial Rp(b−1)(L,T)R_p^{(b-1)}(\mathcal{L},T).

The claim identifies the polynomial obtained from the truncated pp-adic computation with the Euler factor of the associated motive under the stated integrality and nonsingularity conditions. Its resolution is not established in the supplied text.

References

Primary source

Pyry Kuusela, Michael Lathwood, Miroslava Mosso Rojas and Michael Stepniczka, “Solutions of Calabi-Yau Differential Operators as Truncated p-adic Series and Efficient Computation of Zeta Functions”, arXiv:2604.01191 (2026).

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.