4 citations · 7 across the 5 of their papers we have counts for
6 papers
On the representation of quadratic forms by quadratic forms
Rainer Dietmann, Michael Harvey
Using the circle method, we show that for a fixed positive definite integral quadratic form , the expected asymptotic formula for the number of representations of a positive def…
Random diophantine equations, I
Jörg Brüdern, Rainer Dietmann
We consider additive diophantine equations of degree in variables and establish that whenever then almost all such equations satisfy the Hasse principle. The eq…
Hilbert cubes in progression-free sets and in the set of squares II
Rainer Dietmann, Christian Elsholtz
Let be the set of integer squares. We show that the dimension of a Hilbert cube is bounded by
On Gaps Between Primitive Roots in the Hamming Metric
Rainer Dietmann, Christian Elsholtz, Igor E. Shparlinski
We consider a modification of the classical number theoretic question about the gaps between consecutive primitive roots modulo a prime , which by the well-known result of Burge…
Least zero of a cubic form
T. D. Browning, R. Dietmann, P. D. T. A. Elliott
An effective search bound is established for the least non-trivial integer zero of an arbitrary integral cubic form in at least 17 variables.
Solubility of Fermat equations
T. D. Browning, R. Dietmann
The arithmetic of ternary diagonal equation is considered for degree d >1, with the outcome that the set of coefficients for which the equation admits a non-zero integer solution i…