Witt Vectors and a Question of Entin, Keating, and Rudnick

Witt Vectors and a Question of Rudnick and Waxman

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.

Witt 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[[...

On Two Questions of Entin, Keating, and Rudnick on Primitive Dirichlet Characters

This is Part II of the paper “A question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor” [Ka-QKRPD]. Here we prove two independence results for tuples of character sums, either formed with a variable character and its powers, or formed with two characters and their product.

On a Question of Keating and Rudnick about Primitive Dirichlet Characters with Squarefree Conductor

We prove equidistribution results, in the function field setting, for the L-functions attached to primitive, odd Dirichlet characters with a fixed squarefree conductor.

The Variance of the Number of Prime Polynomials in Short Intervals and in Residue Classes