O sedmnáctém Hilbertově problému
Obere Abschätzung für die Anzahl der B-Zwillinge auf kurzen Intervallen.
On a problem of sums of mixed powers
On an additive problem of unlike powers in short intervals
We prove that almost all positive even integers can be represented as with for . As a consequence, we show that each sufficiently large odd integer can be written as with for .
On another sieve method and the numbers that are a sum of two hth powers: II.
On binary quartic forms.
On certain additive representations of integers
On Equivalence of Ideals of Real Global Analytic Functions and the 17th Hilbert Problem.
On exponential sums over smooth numbers.
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 pairs of additive cubic equations.
On representations of numbers by sums of squares and quadratic fields
On some topics connected with Waring's problem.
On sums of four cubes of polynomials
On sums of seven cubes of almost primes
On Sums of Squares in etc
On the Bombieri-Korobov estimate for Weyl sums
On the counting function for sums of two squares
On the Fourier coefficients of small positive powers of 0 ... .
On the intervals between numbers that are sums of two squares. III.