The Exceptional Set in Hua’s Theorem for Three Squares of Primes

Jian Liu; Tao Zhan
April 2005
Acta Mathematica Sinica;Apr2005, Vol. 21 Issue 2, p335
Academic Journal
It is proved that with at mostO(N11/12+e) exceptions, all positive integersn=Nsatisfying some necessary congruence conditions are the sum of three squares of primes. This improves substantially the previous results in this direction.


Related Articles

  • Congruence-simple subsemirings of â„š. Kala, Vítĕzslav; Korbelář, Miroslav // Semigroup Forum;Oct2010, Vol. 81 Issue 2, p286 

    Commutative congruence-simple semirings have already been characterized with the exception of the subsemirings of ℝ. Even the class $\mathit{\mathcal{C}ong\mathcal{S}imp}(\mathbb {Q}^{+})$ of all congruence-simple subsemirings of ℚ has not been classified yet. We introduce a new...

  • Growth of Small Generating Sets in SLn(ℤ/pℤ). Gill, Nick; Helfgott, Harald Andrés // IMRN: International Mathematics Research Notices;Sep2011, Vol. 2011 Issue 18, p4226 

    Let G=SLn and fix δ a positive number. We prove that there are positive numbers ε and C such that, for all fields (p prime), and all sets A⊂G(K) that generate G(K), either |A|0 or |A⋅A⋅A|≥C|A|1+ε.

  • On the class of groups with pronormal hall Ï€-subgroups. Guo, W.; Revin, D. // Siberian Mathematical Journal;May2014, Vol. 55 Issue 3, p415 

    Given a set π of prime numbers, we define the class [InlineMediaObject not available: see fulltext.] of all finite groups in which Hall π-subgroups exist and are pronormal by analogy with the Hall classes [InlineMediaObject not available: see fulltext.], [InlineMediaObject not available:...

  • A Biordered Set Representation of Regular Semigroups. Yu, Bing; Xu, Mang // Acta Mathematica Sinica;Apr2005, Vol. 21 Issue 2, p289 

    In this paper, for an arbitrary regular biordered setE, by using biorder-isomorphisms between the ?-ideals ofE, we construct a fundamental regular semigroupWE called NH-semigroup ofE, whose idempotent biordered set is isomorphic toE. We prove further thatWE can be used to give a new...

  • On Prime Factors of An - 1. Tsuneo Ishikawa; Nobuhiko Ishida; Yoshito Yukimoto // American Mathematical Monthly;Mar2004, Vol. 111 Issue 3, p243 

    This article discusses some properties of prime factors of the function An - 1, where A is greater than 1 and n are positive integers, and give some application of them. Some sets of primes that generally arise are given and explained for educat

  • Classification of some Ï„-congruence-free completely regular semigroups. Yu, Houyi; Wang, Zhengpan; Wu, Tongsuo; Ye, Meng // Semigroup Forum;Apr2012, Vol. 84 Issue 2, p308 

    Let Ï„ be an equivalence relation on a semigroup. We introduce Ï„-congruence-free semigroups, extending the notion of congruence-free semigroups, and classify all completely regular semigroups which are Ï„-congruence-free, where Ï„ is one of Green's relations...

  • Coset extensions of S-sets. Grillet, P.A. // Acta Mathematica Hungarica;2005, Vol. 106 Issue 4, p301 

    Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of...

  • Congruences on Additive Inverse Semirings. Maity, S. K. // Southeast Asian Bulletin of Mathematics;2006, Vol. 30 Issue 3, p473 

    We introduce the concepts of normal ideal and normal congruence on an additive inverse semiring. Also the concepts of congruence pair and kernel normal system for an additive inverse semiring are introduced. The least skew-ring congruence, Clifford congruence and generalized Clifford congruence...

  • On right congruences of semigroups having no proper essential right congruences. Wu, Chong-Yih // Semigroup Forum;Oct2012, Vol. 85 Issue 2, p369 

    A right congruence ρ in a semigroup S is essential if for any right congruence σ we have ρ∧ σ= ι (the identity relation) implies σ= ι. Clearly, the universal relation, ν, is an essential right congruence. We say ρ is proper if ρ≠ ν. In this paper we...


Read the Article


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

Try another library?
Sign out of this library

Other Topics