4 citations · 4 across the 5 of their papers we have counts for
5 papers
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…
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…
Bernstein--Sato Theory for D-modules in Positive Characteristic
Daichi Takeuchi
In this article, we develop a positive characteristic analogue of the Bernstein--Sato theory for holonomic D-modules in the complex setting. We work with D-modules on a Noetherian…
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-…
Gauss sums and Van der Geer--Van der Vlugt curves
Daichi Takeuchi, Takahiro Tsushima
We study Van der Geer--Van der Vlugt curves in a ramification-theoretic view point. We give explicit formulae on L-polynomials of these curves. As a result, we show that these curv…