On two problems of E. M. Robinson about sums of roots of unity
On two-primary algebraic K-theory of quadratic number rings with focus on K₂
On type numbers of split orders of definite quaternion algebras.
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1
On units and fundamental units.
On units of some fields of the form
Let and be two prime integers and let be a positive odd square-free integer. Assuming that the fundamental unit of has a negative norm, we investigate the unit group of the fields .
On Unramified Galois Extensions Over Maximum Abelian Extensions of Algebraic Number Fields.
On valued function fields II. Regular functions and elements with the uniqueness property.
On values of L-functions of totally real algebraic number fields at integers
On values of the Mahler measure in a quadratic field (solution of a problem of Dixon and Dubickas)
On Values of Zeta Functions and ?-adic Euler Characteristc.
On Waring's problem in algebraic number fields
On Waring's problem in algebraic number fields
On Washington group of circular units of some composita of quadratic fields
On wild ramification in quaternion extensions
This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain (along with some partial results for the more general case). This catalog depends upon the refined ramification filtration, which as defined in [2] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare...
On zeroes of the twisted tensor L-function.
Optimality of the Width- Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases
We consider digit expansions with an endomorphism of an Abelian group. In such a numeral system, the -NAF condition (each block of consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight admits an optimal -NAF).This result is then applied to imaginary quadratic bases, which are used for scalar multiplication in elliptic...
Orbit-cone correspondence for the proalgebraic completion of normal toric varieties
We prove that there is an orbit-cone correspondence for the proalgebraic completion of normal toric varieties, which is analogous to the classical orbit-cone correspondence for toric varieties.
Orders, in non-Eichler (R)-algebras over global function fields, having the cancellation property.