On elementary lower bounds for the partition function.
On Equivalence of Ideals of Real Global Analytic Functions and the 17th Hilbert Problem.
On Estermann's proof of a theorem of Minkowski
On exponential sums over smooth numbers.
On Generalized Quadratic Equations in Three Prime Variables.
On Goldbach's problem
On higher-power moments of Δ(x)
On Hilbert’s solution of Waring’s problem
In 1909, Hilbert proved that for each fixed k, there is a number g with the following property: Every integer N ≥ 0 has a representation in the form N = x 1k + x 2k + … + x gk, where the x i are nonnegative integers. This resolved a conjecture of Edward Waring from 1770. Hilbert’s proof is somewhat unsatisfying, in that no method is given for finding a value of g corresponding to a given k. In his doctoral thesis, Rieger showed that by a suitable modification of Hilbert’s proof, one can give explicit...
On indefinite diagonal forms in many variables.
On integer points in polygons
The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the -dilatation, , of certain classes of irrational polygons the error terms are bounded as with some , or as with arbitrarily small .
On integers of the form
On lattice points in large convex bodies
On Linnik's approximation to Goldbach's problem, I
On Linnik's theorem on Goldbach numbers in short intervals and related problems
Linnik proved, assuming the Riemann Hypothesis, that for any , the interval contains a number which is the sum of two primes, provided that is sufficiently large. This has subsequently been improved to the same assertion being valid for the smaller gap , the added new ingredient being Selberg’s estimate for the mean-square of primes in short intervals. Here we give another proof of this sharper result which avoids the use of Selberg’s estimate and is therefore more in the spirit of Linnik’s...
On Mirsky's generalisation of a problem of Evelyn-Linfoot and Page in additive theory of numbers.
On multiperiodic infinite recursions and their finite core.
On new partition of numbers
On nonary cubic forms.
On nonary cubic forms: II.
On nonary cubic forms: III.