7 citations · 11 across the 10 of their papers we have counts for
10 papers
Expander estimates for cubes
Joerg Bruedern, Simon L Rydin Myerson
If is a set of natural numbers of exponential density , then the exponential density of all numbers of the form with and is…
Pairs of diagonal quartic forms: the asymptotic formulae
Joerg Bruedern, Trevor D. Wooley
We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in or more variables. In certain cases, pairs…
Partitio Numerorum: sums of a prime and a number of -th powers
Joerg Bruedern, Trevor D. Wooley
Let be a natural number and let be the unique real solution of the equation in . Then, when , we establish an asymp…
On Waring's problem for larger powers
Joerg Bruedern, Trevor D. Wooley
Let denote the least number having the property that every sufficiently large natural number is the sum of at most positive integral -th powers. Then for all $k\i…
On smooth Weyl sums over biquadrates and Waring's problem
Joerg Bruedern, Trevor D. Wooley
We provide estimates for moments of biquadratic smooth Weyl sums, when , by enhancing the second author's iterative method that delivers estimates beyon…
A paucity problem for certain triples of diagonal equations
Joerg Bruedern, Trevor D. Wooley
We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means of a complification argument, we obtain an a…
An instance where the major and minor arc integrals meet
Joerg Bruedern, Trevor D. Wooley
We apply the circle method to obtain an asymptotic formula for the number of integral points on a certain sliced cubic hypersurface related to the Segre cubic. Unusually, the major…
Correlation estimates for sums of three cubes
Joerg Bruedern, Trevor D. Wooley
We establish estimates for linear correlation sums involving sums of three positive integral cubes. Under appropriate conditions, the underlying methods permit us to establish the…
Cubic moments of Fourier coefficients and pairs of diagonal quartic forms
Joerg Bruedern, Trevor D. Wooley
We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensi…
Subconvexity for additive equations: pairs of undenary cubic forms
Joerg Bruedern, Trevor D. Wooley
We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the nu…