On the Siegel formula for ternary skew-hermitian forms

∗-Valuations and Hermitian Forms on Skew Fields

This paper is a survey of the literature on ways in which the concept of ordering can be extended to the setting of a division ring with involution and the main results for these extensions.

Strictly regular ternary Hermitian forms

Article history: Received 28 October 2015 Received in revised form 8 April 2016 Accepted 9 April 2016 Communicated by David Goss MSC: primary 11E39 secondary 11E12, 11E20

Cohomological Invariants of Quaternionic Skew-hermitian Forms

We define a complete system of invariants en,Q, n ≥ 0 for quaternionic skew-hermitian forms, which are twisted versions of the invariants en for quadratic forms. We also show that quaternionic skew-hermitian forms defined over a field of 2-cohomological dimension at most 3 are classified by rank, discriminant, Clifford invariant and Rost invariant.

On the Riemann-Siegel formula

In this article we derive a generalization of the Riemann-Siegel asymptotic formula for the Riemann zeta function. By subtracting the singularities closest to the critical point we obtain a significant reduction of the error term at the expense of a few evaluations of the error function. We illustrate the efficiency of this method by comparing it to the classical Riemann-Siegel formula.

On Modified Hermitian and Skew - Hermitian Splitting