Theorems in the additive theory of numbers

@article{Bose1962TheoremsIT,
  title={Theorems in the additive theory of numbers},
  author={R. C. Bose and Sarvadaman Chowla},
  journal={Commentarii Mathematici Helvetici},
  year={1962},
  volume={37},
  pages={141-147}
}
SummaryThis paper extends some earlier results on difference sets andB2 sequences bySinger, Bose, Erdös andTuran, andChowla. 
View on Springer
repository.lib.ncsu.edu
186 Citations
Highly Influential Citations
18
Background Citations
48
Methods Citations
23
Results Citations
2

186 Citations

Citation Type

Citation Type

0 Ju n 20 07 On Montgomery ’ s 13 th problem
We use an estimate for character sums over finite fields of Katz to solve open problems of Montgomery and Turán. Let h ≥ 2 be an integer. We prove that inf |z k |≥1
Nonabelian sets with distinct k-sums
A New Upper Bound for B2[2] Sets
  • A. Plagne
  • Mathematics
    J. Comb. Theory, Ser. A
  • 2001
A new upper bound for the cardinality of finite B22] sets is obtained, namely F2(N, 2)<2.363584N for N sufficiently large. This improves on a recent result by Cilleruelo.
On some problems in the theory of finite fields
TLDR
The construction of irreducible and primitive polynomials and some new applications of the theory of finite fields References are presented.
Addition of Sequences: Study of Representation Functions by Number Theoretic Methods
As in Chapter I (see the beginning of § 1 of Chapter I), we use A to denote a subsequence of the sequence ℒ0, of non-negative integers. Although our principal investigations concern infinite…
DENSE INFINITE Bh SEQUENCES
For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x√(h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences.
Sidon Sets
  • H. Abbott
  • Mathematics
    Canadian Mathematical Bulletin
  • 1990
Abstract Denote by g(n) the largest integer m such that every set of integers of size n contains a subset of size m whose pairwise sums are distinct. It is shown that g(n) > cn1/2 for any constant c…
Lattice Packings of Cross-polytopes Constructed from Sidon Sets
A family of lattice packings of n-dimensional cross-polytopes (l1 balls) is constructed by using the notion of Sidon sets in finite Abelian groups. The resulting density exceeds that of any prior…
On the Subsets Product in Finite Groups
On some power sum problems of Montgomery and Turan
TLDR
An estimate for character sums over finite fields of Katz is used to solve open problems of Montgomery and Turan and improves on a bound of Erdos-Renyi by a factor of the order sqrt log n.
...
...

References

SHOWING 1-3 OF 3 REFERENCES
On a problem of sidon in additive number theory, and on some related problems
To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question…
On the difference between consecutive primes
[Received 3 August 1937] 1. LET pn denote the nth. prime, and 77(2;) the number of primes p not exceeding x. The existence of an absolute constant 6 < 1 such that a (1) n(x) ~ . log a; when x -> 00,…
A theorem in finite projective geometry and some applications to number theory
A point in a finite projective plane PG(2, pn), may be denoted by the symbol (Xl, X2, X3), where the coordinates x1, X2, X3 are marks of a Galois field of order pn, GF(pn). The symbol (0, 0, 0) is…