Combinatorial sieves of dimension exceeding one

  title={Combinatorial sieves of dimension exceeding one},
  author={Harold G. Diamond and Heini Halberstam and H. E. Richert},
  journal={Journal of Number Theory},
The Hyperbolic Lattice Point Count in Infinite Volume with Applications to Sieves
We develop novel techniques using abstract operator theory to obtain asymptotic formulae for lattice counting problems on infinite-volume hyperbolic manifolds, with error terms which are uniform as
Almost prime coordinates for anisotropic and thin pythagorean orbits
We make an observation which doubles the exponent of distribution in certain Affine Sieve problems, such as those considered by Liu-Sarnak, Kontorovich, and Kontorovich-Oh. As a consequence, we
Almost primes represented by binary forms
We demonstrate that, under suitable local conditions on a finite collection F1,…, Fg of binary irreducible forms with integer coefficients, the product F1(x)·…·Fg(x) will have at most r prime factors
Bounds on entries in Bianchi group generators
. Upper and lower bounds are given for the maximum Euclidean curvature among faces in Bianchi’s fundamental polyhedron for PSL 2 ( (cid:79) ) in the upper-half space model of hyperbolic space, where
A Boundary Value Problem for a Pair of Differential Delay Equations Related to Sieve Theory, I
Abstract The authors′ combinatorial sieve theory is based in part on solving a pair of simultaneous differential delay equations that are subject to several initial conditions and conditions at
A comparison of two sieves, I
This work shows the interrelation between some measures of the quality of the sieves, shows that the DHR upper sieve is at most of the size of that of AO at the point where the upper estimates first can deviate, and obtains a new lower bound for the sieving limit of the D HR sieve for large values of к.
On the Sieve Parameters a ? and ? for Large ?
Abstract Two parameters,ακandβκ, play a central role in the sieve method of Diamond, Halberstam, and Richert. For each value of the sieve dimensionκ>1,ακis the point beyond which the DHR upper sieve
Gauss ’ s three squares theorem with almost prime variables
Current technology apparently lacks the power to establish this conjecture. However, various approximations to it have been studied. Let E(N) denote the number of all positive integers n ≤ N
Almost prime Pythagorean triples in thin orbits
Abstract For the ternary quadratic form Q(x) = x2 + y2 − z2 and a non-zero Pythagorean triple x0 ∈ ℤ3 lying on the cone Q(x) = 0, we consider an orbit 𝒪 = x0Γ of a finitely generated subgroup Γ <


Elementary and analytic theory of numbers
These are the proceedings of the 20th semester held at the Banach International Mathematical Center at Warsaw from September 1st to November 13th, 1982
On Bombieri's asymptotic sieve
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » ( implique l’accord avec les conditions
IWANIEC, On Bombieri’s asymptotic sieve, Ann
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RICHERT. “Sieve Methods,
  • 1974
Selberg's sieve estimate with a one sided hypothesis
Lectures on the Linear Sieve: “Topics in Analytic Number Theory,
  • 1985
Lectures on the Sieve Method and Prime Number Theory,
  • Tata Institute for Fundamental Research,
  • 1983
Number theory