A unitary criterion for p-adic groups.
A valuation criterion for normal basis generators of Hopf-Galois extensions in characteristic
Let be a finite extension of discrete valuation rings of characteristic , and suppose that the corresponding extension of fields of fractions is separable and is -Galois for some -Hopf algebra . Let be the different of . We show that if is totally ramified and its degree is a power of , then any element of with generates as an -module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. G. Elder for Galois extensions.
A van der Waerden variant.
A Vanishing Theorem for Power Series.
A variant of Selberg's asymptotic formula.
A variation on perfect numbers.
A variety of Euler's sum of powers conjecture
We consider a variety of Euler’s sum of powers conjecture, i.e., whether the Diophantine system has positive integer or rational solutions , , , , Using the theory of elliptic curves, we prove that it has no positive integer solution for , but there are infinitely many positive integers such that it has a positive integer solution for . As a corollary, for and any positive integer , the above Diophantine system has a positive rational solution. Meanwhile, we give conditions such that...
A way of Reducing the Factorization Problem in Z[x] to the Factorization Problem in Z
A weak Hasse principle for central simple algebras with an involution.
A weak Néron model with applications to -adic dynamical systems
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
A weakening of the euclidean property for integral domains and applications to algebraic number theory. I.
A weighted sieve of Brun's type
A weighted sieve of Greaves' type I
A weighted sieve of Greaves' type II
A well-rounded linear function.
A Wirsing-type approach to some continued fraction expansion.
A WZ proof of a “curious” identity.
A zero density result for the Riemann zeta function
We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
A χ-analogue of a formula of Ramanujan for ζ(1/2)