27 citations · 57 across the 15 of their papers we have counts for
16 papers
Estimates for smooth Weyl sums on major arcs
Joerg Bruedern, Trevor D. Wooley
We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy-Littlewood method. In particular, we derive mean value estimates on major arcs f…
Partitio Numerorum: sums of squares and higher powers
Joerg Bruedern, Trevor D. Wooley
We survey the potential for progress in additive number theory arising from recent advances concerning major arc bounds associated with mean value estimates for smooth Weyl sums. W…
On the distribution of powered numbers
Jörg Brüdern, Olivier Robert
Asymptotic formulae are established for the number of natural numbers with largest square-free divisor not exceeding , for any fixed positive parameter $\varthet…
On Waring's problem: beyond Freiman's theorem
Joerg Bruedern, Trevor D. Wooley
Let satisfy . Freiman's theorem shows that when , there exists such that all large i…
The Manin-Peyre conjecture for smooth spherical Fano threefolds
Valentin Blomer, Jörg Brüdern, Ulrich Derenthal +1
The Manin-Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, th…
The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
Valentin Blomer, Jörg Brüdern, Ulrich Derenthal +1
The Manin-Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as wel…
Common divisors of totients of polynomial sequences
J. Brüdern, K. Soundararajan
Motivated by a question of Venkataramana, we consider the greatest common divisor of where is a primitive polynomial with integer coefficients, and ranges over al…
The Manin-Peyre conjecture for a certain biprojective cubic threefold
Valentin Blomer, Jörg Brüdern, Per Salberger
The conjectures of Manin and Peyre are confirmed for a certain threefold.
Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations
Joerg Bruedern, Trevor D. Wooley
We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition. Our methods employ the a…
Counting in hyperbolic spikes: the diophantine analysis of multihomogeneous diagonal equations
Valentin Blomer, Jörg Brüdern
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available…
The Hasse principle for systems of diagonal cubic forms
Joerg Bruedern, Trevor D. Wooley
We establish the Hasse Principle for systems of r simultaneous diagonal cubic equations whenever the number of variables exceeds 6r and the associated coefficient matrix contains n…
On a senary cubic form
Valentin Blomer, Jörg Brüdern, Per Salberger
A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.
Piatetski-Shapiro sequences
Roger C. Baker, William D. Banks, Jörg Brüdern +2
We consider various arithmetic questions for the Piatetski-Shapiro sequences $\fl{n^c}$ () with , . We exhibit a positive function with the pro…
Random Diophantine inequalities of additive type
Jörg Brüdern, Rainer Dietmann
Using the Davenport-Heilbronn circle method, we show that for almost all additive Diophantine inequalities of degree in more than variables the expected asymptotic formula…
Random diophantine equations of additive type
Jörg Brüdern, Rainer Dietmann
Using the circle method in combination with lattice point counting arguments, we show that for almost all homogeneous diophantine equations of additive type and degree in more…
The Hasse principle for pairs of diagonal cubic forms
J. Bruedern, T. D. Wooley
By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of…