An Introduction to the Linnik Problems

Equidistribution, L-functions and Ergodic theory: on some problems of Yu. V. Linnik

An old question of Linnik asks about the equidistribution of integral points on a large sphere. This question proved to be very rich: it is intimately linked to modular forms, to subconvex estimates for L-functions, and to dynamics of torus actions on homogeneous spaces. Indeed, Linnik gave a partial answer using ergodic methods, and his question was completely answered by Duke using harmonic a...

Linnik ’ s approximation to Goldbach ’ s conjecture , and other problems

We examine the problem of writing every sufficiently large even number as the sum of two primes and at most K powers of 2. We outline an approach that only just falls short of improving the current bounds on K. Finally, we improve the estimates in other Waring–Goldbach problems.

Improvement of a Theorem of Linnik and Walfisz 423 Improvement of a Theorem of Linnik and Walfisz

On a Result of Vinogradov and Linnik

In this paper, considering the concept of Universal Multiplication Table, we show that for every n ≥ 2, the inequality: M(n) = #{ij|1 ≤ i, j ≤ n} ≥ n2 N(n2) , holds true with: N(n) = n log 2 log log n ( 1+ 387 200 log log n ) . Then using this fact we show that the value c in the Linnik-Vinogradov’s result; M(n) = O (

A general recursive formula for the discrete stable and Linnik distributions and a family of extensions

The purpose of this paper is to present a general method to compute recursively the probability mass function of the discrete stable, discrete Linnik and discrete Mittag-Le­ er distribution. The recursive computation method is based on the representation of these distributions as compound distributions and on the Panjer algorithm (see Panjer (1981), Klugman et al. (1998) or Rolski et al. (1999)...