Waring’s problem with digital restrictions

A central limit theorem for integer partitions

“…Numbers whose b-ary sum of digits has to satisfy a certain congruence have been studied by Gel'fond [10] and Mauduit and Sárközy [14]. Their additive properties have been discussed in a paper by Thuswaldner and Tichy [20] and subsequent papers. This is actually an example for which there is only a single pole: it is not difficult to show that the Dirichlet series associated with the set of all integers whose b-ary sum of digits is ≡ h mod k is essentially 1 k ζ(s).…”

Waring’s problem with restrictions on q-additive functions

“…Having proved this theorem, one can obtain the following result in literally the same way as in [6] and finally prove Theorem 2.1 by means of the circle method. The original version of the proof given in [6] was modified by P f e i f f e r and T h u s w a l d n e r in [5] -they used the results of F o r d [2] to improve the bound for s from 2 k to k 2 (log k + log log k+O (1)). Their proof can easily be adapted to the current problem.…”

Waring’s problem with digital restrictions in $$ \mathbb{F} $$ q[X]

“…The proof of Theorem 1.2 makes use of the circle method and we mainly follow Webb [15] and Thuswaldner and Tichy [13]. We adopt their method and denote by R(N ) := R (N, n, s, k, J, M, q) the number of solutions of the equation…”

“…In the present paper we want to show a generalization of a result due to Thuswaldner and Tichy [13] to the ring of polynomials over a finite field. In a recent paper they could prove that for fixed positive integers j and m every sufficiently large positive integer N has a representation of the form…”