On Waring's Problem in p-adic fields
On Waring's problem: two cubes and two minicubes
On Waring's problem with polynomial summands
On Waring's problem with polynomial summands II
On Waring's problem with polynomial summands II: Addendum
On Waring's problem with quartic polynomial summands
On Washington group of circular units of some composita of quadratic fields
On weak automorphs of binary forms over an arbitrary field [Book]
On weak uniform distribution of sequences of integers
On weighted densities
The continuity of densities given by the weight functions , , with respect to the parameter is investigated.
On well distribution modulo 1 and systems of numeration
On Wendt's determinant and Sophie Germain's theorem.
On Weyl's inequality and Waring's problem for cubes
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 Witt rings of function fields of real analytic surfaces and curves.
Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points, in the two-dimensional...
On Witten multiple zeta-functions associated with semisimple Lie algebras I
We define Witten multiple zeta-functions associated with semisimple Lie algebras , of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case , we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations, we prove...
On and
The two related Diophantine equations: and , have infinitely many nontrivial, primitive integral solutions. We give two parametric solutions, one for each of these equations.
On
In p. 219 of R.K. Guy’s Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation has no integer solutions with and . But, contrary to this expectation, we show that for , this equation has infinitely many primitive integer solutions, i.e. the solutions satisfying the condition .
On x³ + y³ + z³ = 3μxyz and Jacobi polynomials
On zero free sets.