## 33 Citations

The Hyperbolic Lattice Point Count in Infinite Volume with Applications to Sieves

- Mathematics
- 2007

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

- Mathematics
- 2014

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

- Mathematics
- 2010

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

- Mathematics
- 2021

Upper and lower bounds are given for the maximum Euclidean curvature among faces in Bianchi’s fundamental polyhedron for PSL2(O) in the upper-half space model of hyperbolic space, where O is an…

A Boundary Value Problem for a Pair of Differential Delay Equations Related to Sieve Theory, I

- Mathematics
- 1993

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

- MathematicsPeriod. Math. Hung.
- 2002

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 ?

- Mathematics
- 1997

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

- Mathematics
- 2007

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

- Mathematics
- 2010

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 <…

## References

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- Mathematics
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These are the proceedings of the 20th semester held at the Banach International Mathematical Center at Warsaw from September 1st to November 13th, 1982

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- Mathematics
- 1978

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions…

IWANIEC, On Bombieri’s asymptotic sieve, Ann

- Scu. Norm. Sup.-Pisa (IV)
- 1978

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- Tata Institute for Fundamental Research,
- 1983