منابع مشابه
On variants of the larger sieve
The large sieve has its origins in the work of Linnik and Rényi. It was developed to deal with sequences that avoid a positive proportion of residue classes. It was later simplified by Roth, Bombieri, Davenport, Halberstam, Montgomery, Gallagher and many others. For a survey see Montgomery [12] and Bombieri [1]. It is known that Montgomery’s large sieve [12] is a useful method when sifting sequ...
متن کاملHilbert’s Irreducibility Theorem and the Larger Sieve
We describe an explicit version of Hilbert’s irreducibility theorem using a generalization of Gallagher’s larger sieve. We give applications to the Galois theory of random polynomials, and to the images of the adelic representation associated to elliptic curves varying in rational families.
متن کاملA General Polynomial Sieve
An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve to aid in finding smooth Coppersmith polynomials for use in the index calculus method. We discuss their approach and some of the difficulties they found with their sieve. We present a new sieving method that can be a...
متن کاملA Sieve Auxiliary Function
In the sieve theories of Rosser-Iwaniec and Diamond-Halberstam-Richert, the upper and lower bound sieve functions (F and f, respectively) satisfy a coupled system of diierential-diierence equations with retarded arguments. To aid in the study of these functions, Iwaniec introduced a conjugate diierence-diierential equation with an advanced argument, and gave a solution, q, which is analytic in ...
متن کاملDrops impacting a sieve.
We study experimentally the impact of liquid drops against thin plates pierced with small holes. When the drop is larger than the hole, different situations can occur: (i) at a small velocity, the drop is entirely captured by the plate; (ii) above a threshold speed, some liquid is ejected below the surface. We characterize this critical speed and these two different situations, focusing on the ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1971
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-18-1-77-81