Almost primes represented by binary forms

Marasingha, Gihan
October 2010
Journal of the London Mathematical Society;Oct2010, Vol. 82 Issue 2, p295
Academic Journal
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 for infinitely many x. We give explicit upper bounds for r that depend only on g and on the total degree of the product polynomial.


Related Articles

  • Characterization of binary polynomials of idempotent algebras. Movsisyan, Yu.; Pashazadeh, J. // Journal of Mathematical Sciences;Nov2012, Vol. 186 Issue 5, p802 

    In this paper, we characterize the set of all binary algebraic (or polynomial) operations of an idempotent algebra that has at least one r-ary algebraic operation, ( r ≥ 2), depending on every variable such that there is no an ( r+2)-ary algebraic operation depending on at least ( r+1)...

  • Tight Relative 2- and 4-Designs on Binary Hamming Association Schemes. Li, Zengti; Bannai, Eiichi; Bannai, Etsuko // Graphs & Combinatorics;Jan2014, Vol. 30 Issue 1, p203 

    The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte (Philips Res Rep 32:373-411, ). We formulate Fisher type lower bounds as well as the concept of tight relative 2- and 4-designs very explicitly for binary Hamming association schemes H( n, 2). Then we...

  • Strengthened semidefinite programming bounds for codes. Laurent, Monique // Mathematical Programming;Feb2007, Vol. 109 Issue 2/3, p239 

    We give a hierarchy of semidefinite upper bounds for the maximum size A( n, d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de...

  • Property of right units of complete semigroups of binary relations defined by finite XI-semilattices of unions. Diasamidze, Ya. // Journal of Mathematical Sciences;Nov2012, Vol. 186 Issue 5, p720 

    We study properties of right units of complete semigroups of binary relations defined by finite XI-semilattices of unions.

  • Complete semigroups of binary relations defined by finite XI-semilattices of unions. Diasamidze, Ya.; Makharadze, Sh. // Journal of Mathematical Sciences;Nov2012, Vol. 186 Issue 5, p723 

    We give conditions under which the X-semilattice of unions is an XI-semilattice, i.e., let D be a finite X-semilattice of unions. The complete semigroup of binary relation B( D) is defined by the XI-semilattice of unions if and only if V ( D, β) = D for some β ∈ B( D).

  • On Spechtian varieties of right alternative algebras. Kuz’min, A. // Journal of Mathematical Sciences;Feb2008, Vol. 149 Issue 2, p1098 

    A sufficient condition is proved for the Specht property of varieties of right alternative metabelian algebras over a field of characteristic distinct from 2. As a consequence, the Specht property of some varieties generated by right alternative metabelian algebras A satisfying a commutator...

  • On new measures of pseudorandomness of binary lattices. Gyarmati, Katalin // Acta Mathematica Hungarica;Jun2011, Vol. 131 Issue 4, p346 

    Hubert, Mauduit and S�rk�zy introduced the pseudorandom measure of order l of binary lattices. This measure studies the pseudorandomness only on box lattices of very special type. In certain applications one may need measures covering a more general situation. In this paper the line...

  • On ( n, m)-semigroups. Zhu, Yongwen // Semigroup Forum;Apr2012, Vol. 84 Issue 2, p342 

    We generalize Green's lemma and Green's theorem for usual binary semigroups to ( n, m)-semigroups, define and describe the regularity for an element of an ( n, m)-semigroup, give some criteria for an element of an ( n, m)-semigroup to be invertible, and further apply the invertibility for ( n,...

  • Subdirectly irreducible state-morphism BL-algebras. Dvurečenskij, Anatolij // Archive for Mathematical Logic;Feb2011, Vol. 50 Issue 1/2, p145 

    Recently Flaminio and Montagna (Proceedings of the 5th EUSFLAT Conference, II: 201-206. Ostrava, 2007), (Inter. J. Approx. Reason. 50:138-152, 2009) introduced the notion of a state MV-algebra as an MV-algebra with internal state. We have two kinds: state MV-algebras and state-morphism...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics