In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 ...In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 and any 0【ε【14,E k(x+H)-E k(x)≤H(log x) -Aholds for x 12-14k+ε≤H≤x, here the implies constant depends at most on A and ε.展开更多
Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:Rk×Rn→Rn. In this paper,we shall discuss two extensions of the theorem.that is,the suff...Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:Rk×Rn→Rn. In this paper,we shall discuss two extensions of the theorem.that is,the sufficient and necessary conditions about the existence of an orthogonal multiplication f:Rk×Rn→Rn+1or f:Rk×Rn→Rn+2展开更多
In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn...In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.展开更多
The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localizati...The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.展开更多
文摘In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
文摘In this paper, we investigate HUA’s Theorem for short intervals under GRH. Let E k(x)=#{{n≤x;2|n,k is odd, n≠p 1+p k 2}∪{n≤x;2|n,2|k,(p-1)|k, n1(modp),n≠p 1+p k 2}}. Assume GRH. For any k≥2, any A】0 and any 0【ε【14,E k(x+H)-E k(x)≤H(log x) -Aholds for x 12-14k+ε≤H≤x, here the implies constant depends at most on A and ε.
文摘Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:Rk×Rn→Rn. In this paper,we shall discuss two extensions of the theorem.that is,the sufficient and necessary conditions about the existence of an orthogonal multiplication f:Rk×Rn→Rn+1or f:Rk×Rn→Rn+2
文摘In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.
基金Project supported by the Cheung-Kong Scholarshipthe Key Laboratory of Pure MathematicsCombinatorics of the Ministry of Education of Chinathe 973 Project of the Ministry of Science and Technology of China.
文摘The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.
