Name
Abstract | ||
|---|---|---|
In this paper we prove that if Q(x,y) = ax(2) + bxy + cy(2) is an integral binary quadratic form with a nonzero, nonsquare discriminant d and if Q represents an arithmetic progression {kn + l : n = 0, 1, ..., R - 1), where k and l are positive integers, then there are absolute constants C-1 > 0 and L-1 > 0 such that R < C(1)l(k(2)vertical bar d vertical bar)(L)(1). Moreover, we prove that every nonzero integral binary quadratic form represents a nontrivial 3-term arithmetic progression infinitely often. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.4169/amer.math.monthly.121.10.932 | AMERICAN MATHEMATICAL MONTHLY |
Field | DocType | Volume |
Integer,Prime (order theory),Discrete mathematics,Binary quadratic form,Square number,Combinatorics,Harmonic progression,Algebra,Discriminant,Mathematics,Arithmetico-geometric sequence,Arithmetic progression | Journal | 121 |
Issue | ISSN | Citations |
10 | 0002-9890 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pallab Kanti Dey | 1 | 0 | 0.34 |
| R. Thangadurai | 2 | 5 | 3.78 |