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math.NT2015★ 4 cited
Simultaneous additive equations: Repeated and differing degrees
Julia Brandes, Scott T. Parsell
We obtain bounds for the number of variables required to establish Hasse principles, both for existence of solutions and for asymptotic formulae, for systems of additive equations…
math.NT2015
Forms representing forms: The definite case
Julia Brandes
Let and be positive definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical repre…
math.NT2015
Sums and differences of power-free numbers
Julia Brandes
We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions to the equations …