An improved upper bound for G(k) in Waring's problem for relatively small k
An infinite family of overpartition congruence modulo 12.
An inverse theorem mod p
An Invitation to Additive Prime Number Theory
2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.
An Omega theorem on differences of two squares.
An -estimate for the number of lattice points in a sphere
Analysis of an algorithm to construct Fibonacci partitions
Another Computation of .... .
Another smallest part function related to Andrews' spt function
We offer some relations and congruences for two interesting spt-type functions, which together form a relation to Andrews' spt function.
Anzahl der Zerlegungen einer ganzen, rationalen Zahl in Summanden, II.
Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden
Appendix to Kazuya Kato: A Hasse principle for two dimensional global fields.
Application of the circle method on multidimensional limit-periodic functions
Applications de la dérivation d'Arbogast à la solution de la partition des nombres et à d'autres problèmes
Approximation of Lebesgue Integrals by Riemann Sums and Lattice Points in Domains with Fractal Boundary.
Arcs containing no three lattice points
Arcs with no more than two integer points on conics
Arithmetic progressions in sums of subsets of sparse sets
Arithmetic progressions in sumsets
1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B always contains an arithmetic progression of length . Our aim is to show that this is not very far from the best possible. Theorem 1. Let ε be a positive number. For every prime p > p₀(ε) there is a symmetric set A of residues mod p such that |A| > (1/2-ε)p and A + A contains no arithmetic progression of length (1.1). A set of residues can be used to get a set of integers in an obvious way. Observe...
Arithmetic progressions of prime-almost-prime twins