Randorn sequences and additive number theory

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Supersequences, Rearrangements of Sequences, and the Spectrum of Bases in Additive Number Theory

The set A = {an}∞n=1 of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If an ∼ αn for some real number α > 0, then α is called an additive eigenvalue of order h. The additive spectrum of order h is the set N (h) consisting of all additive eigenvalues of order h. It is proved that there is a positive nu...

متن کامل

Ergodic Theory and Applications to Additive Number Theory

The following lemma follows the standard paradigm of recurrence results in ergodic theory: given a topological space X which satisfies a suitable ’smallness’ condition (e.g. compactness, μ(X) < ∞), and a transformation T : X → X, there exist points of X which satisfy a certain ’almost-periodicity’ condition under the action of T . Lemma 1. Poincare Recurrence Lemma If (X,β, μ, T ) is an m.p.s. ...

متن کامل

Some Problems in Additive Number Theory

(3) f(x) = (log x/log 2) + 0(1)? 1\Mloser and I asked : Is it true that f(2 11) >_ k+2 for sufficiently large k? Conway and Guy showed that the answer is affirmative (unpublished) . P. Erdös, Problems and results in additive number theory, Colloque, Théorie des Nombres, Bruxelles 1955, p . 137 . 2. Let 1 < a 1< . . . < ak <_ x be a sequence of integers so that all the sums ai,+ . . .+ais, i 1 <...

متن کامل

Fourier Analytic Methods in Additive Number Theory

In recent years, analytic methods have become prominent in additive number theory. In particular, finite Fourier analysis is well-suited to solve some problems that are too difficult for purely combinatorial techniques. Among these is Szemerédi’s Theorem, a statement regarding the density of integral sets and the existence of arithmetic progressions in those sets. In this thesis, we give a gene...

متن کامل

An asymptotic formula in additive number theory

1 . Introduction . In his paper [1], Erdös introduced the sequences of positive integers b 1 < b, < . . ., with (b ;, bj ) = 1, for i ~A j, and 'bi 1 < oo . With any such arbitrary sequence of integers, he associated the sequence {di} of all positive integers not divisible by any bj , and he showed that if b1 > 2, there exists a 0 < 1 (independent of the sequence {b i }) such that d i 1 di < d°...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: MATHEMATICA SCANDINAVICA

سال: 1956

ISSN: 1903-1807,0025-5521

DOI: 10.7146/math.scand.a-10479