Witt Vectors and a Question of Rudnick and Waxman
نویسنده
چکیده
This is Part III of the paper “Witt vectors and a question of Keating and Rudnick” [Ka-WVQKR]. We prove equidistribution results for the L-functions attached to “super-even” characters of the group of truncated “big” Witt vectors, and for the L-functions attached to the twists of these characters by the quadratic character.
منابع مشابه
Witt Vectors and a Question of Entin, Keating, and Rudnick
This is Part II of the paper “Witt vectors and a question of Keating and Rudnick” [Ka-WVQKR]. Here we prove an independence result for tuples of character sums, formed with a variable character and its powers. In the Appendix, we prove an independence result for tuples of character sums formed with variable pairs of characters and products of the two.
متن کاملWitt Vectors and a Question of Keating and Rudnick
Following Keating and Rudnick, we say that a character Λ : B× → C× is “even” if it is trivial on the subgroup k×. The quotient group B×/k× is the group of “big” Witt vectors mod X with values in k. Recall that for any ringA, the groupBigWitt(A) is simply the abelian group 1 +XA[[X]] of formal series with constant term 1, under multiplication of formal series. In this group, the elements 1 +XA[[...
متن کاملWitt rings of quadratically presentable fields
This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...
متن کاملBoolean Witt vectors and an integral Edrei–Thoma theorem
We give explicit descriptions of the Witt vectors of the Boolean semiring. This includes the big Witt vectors, the Schur Witt vectors, and the p-typical Witt vectors. We use this to determine the Schur Witt vectors of the natural numbers, which can be viewed as the classification of totally positive power series with integral coefficients, first observed by Davydov. We also determine the cardin...
متن کاملThe basic geometry of Witt vectors, IThe affine case
We give a concrete description of the category of étale algebras over the ring of Witt vectors of a given finite length with entries in an arbitrary ring. We do this not only for the classical p-typical and big Witt vector functors but also for certain analogues over arbitrary local and global fields. The basic theory of these generalized Witt vectors is developed from the point of view of comm...
متن کامل