Showing math.NTShow all
3 papers · 1 filter
math.NT2026
Factorizations of linearized polynomials and extremal curves in odd characteristic
Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima
We give a complete recipe for constructing extremal van der Geer--van der Vlugt curves over finite fields of odd characteristic. The input data consist of a nonzero element of the…
math.NT2026
Factorization of Additive Polynomials and van der Geer--van der Vlugt curves in characteristic 2
Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima
In our previous work, we gave a formula for the Frobenius eigenvalues of van der Geer--van der Vlugt curves in characteristic 2 by considering suitable quotients of the curve. Alth…
math.NT2025
Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves
Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima
We study exponential sums on Witt vectors, known as Gauss--Heilbronn sums, and the curves whose Frobenius traces realize these sums via a Deligne--Lusztig type construction. For 3-…