17 citations · 30 across the 12 of their papers we have counts for
5 papers · 1 filter
Linear patterns of prime elements in number fields
Wataru Kai
We prove a number field analogue of the Green--Tao--Ziegler theorem on simultaneous prime values of degree 1 polynomials whose linear parts are pairwise linearly independent. Appli…
Notes on Mitsui's Prime Number Theorem with Siegel zeros
Wataru Kai
In these notes, we refine Mitsui's Prime Number Theorem from 1957, which for a number field predicts the number of prime elements in a bounded convex set in $K \otimes _{\mathb…
The Green-Tao theorem for affine curves over F_q
Wataru Kai
Green and Tao famously proved in a 2008 paper that there are arithmetic progressions of prime numbers of arbitrary lengths. Soon after, analogous statements were proved by Tao for…
Constellations in prime elements of number fields
Wataru Kai, Masato Mimura, Akihiro Munemasa +2
Given any number field, we prove that there exist arbitrarily shaped constellations consisting of pairwise non-associate prime elements of the ring of integers. This result extends…
A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map
Wataru Kai
We present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties over -adic fields in terms of the Néron-Severi gro…