共查询到20条相似文献,搜索用时 46 毫秒
1.
D. Bazzanella 《Acta Mathematica Hungarica》2007,116(3):197-207
A well known conjecture about the distribution of primes asserts that between two consecutive squares there is always at least
one prime number. The proof of this conjecture is quite out of reach at present, even under the assumption of the Riemann
Hypothesis. This paper is concerned with the distribution of prime numbers between two consecutive powers of integers, as
a natural generalization of the afore-mentioned conjecture.
相似文献
2.
Artin's primitive root conjecture for function fields was proved by Bilharz in his thesis in 1937, conditionally on the proof of the Riemann hypothesis for function fields over finite fields, which was proved later by Weil in 1948. In this paper, we provide a simple proof of Artin's primitive root conjecture for function fields which does not use the Riemann hypothesis for function fields but rather modifies the classical argument of Hadamard and de la Vallée Poussin in their 1896 proof of the prime number theorem. 相似文献
3.
Roger Behling Gabriel Haeser Alberto Ramos Daiana S. Viana 《Journal of Optimization Theory and Applications》2018,176(3):625-633
In this paper, we deal with a conjecture formulated in Andreani et al. (Optimization 56:529–542, 2007), which states that whenever a local minimizer of a nonlinear optimization problem fulfills the Mangasarian–Fromovitz constraint qualification and the rank of the set of gradients of active constraints increases at most by one in a neighborhood of the minimizer, a second-order optimality condition that depends on one single Lagrange multiplier is satisfied. This conjecture generalizes previous results under a constant rank assumption or under a rank deficiency of at most one. We prove the conjecture under the additional assumption that the Jacobian matrix has a smooth singular value decomposition. Our proof also extends to the case of the strong second-order condition, defined in terms of the critical cone instead of the critical subspace. 相似文献
4.
Christopher Daw 《Archiv der Mathematik》2012,98(5):433-440
In this paper we give a short proof of the André-Oort conjecture for products of modular curves under the Generalised Riemann
Hypothesis using only simple Galois-theoretic and geometric arguments. We believe this method represents a strategy for proving
the conjecture for a general Shimura variety under GRH without using ergodic theory. We also demonstrate a short proof of
the Manin–Mumford conjecture for Abelian varieties using similar arguments. 相似文献
5.
Michael Jöllenbeck 《Journal of Pure and Applied Algebra》2006,207(2):261-298
In this paper we study the multigraded Hilbert and Poincaré-Betti series of A=S/a, where S is the ring of polynomials in n indeterminates divided by the monomial ideal a. There is a conjecture about the multigraded Poincaré-Betti series by Charalambous and Reeves which they proved in the case where the Taylor resolution is minimal. We introduce a conjecture about the minimal A-free resolution of the residue class field and show that this conjecture implies the conjecture of Charalambous and Reeves and, in addition, gives a formula for the Hilbert series. Using Algebraic Discrete Morse theory, we prove that the homology of the Koszul complex of A with respect to x1,…,xn is isomorphic to a graded commutative ring of polynomials over certain sets in the Taylor resolution divided by an ideal r of relations. This leads to a proof of our conjecture for some classes of algebras A. We also give an approach for the proof of our conjecture via Algebraic Discrete Morse theory in the general case.The conjecture implies that A is Golod if and only if the product (i.e. the first Massey operation) on the Koszul homology is trivial. Under the assumption of the conjecture we finally prove that a very simple purely combinatorial condition on the minimal monomial generating system of a implies Golodness for A. 相似文献
6.
It is generally known that under the generalized Riemann hypothesis one could establish the Goldbach conjecture by the circle method provided one could obtain a certain estimate for the integral of the representation function over the minor arcs. Here it is first shown that the generalized Riemann hypothesis in the above statement can be weakened to the assumption that Siegel zeros do not exist. The case when Siegel zeros do exist is then considered. 相似文献
7.
The Gross conjecture over ? was first claimed by Aoki in 1991. However, the original proof contains too many mistakes and false claims to be considered as a serious proof. This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki. We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of ?. 相似文献
8.
《中国科学 数学(英文版)》2010,(9)
The Gross conjecture over Q was first claimed by Aoki in 1991.However,the original proof contains too many mistakes and false claims to be considered as a serious proof.This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki.We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of Q. 相似文献
9.
Günter M. Ziegler 《Inventiones Mathematicae》2002,147(3):671-691
The Kneser conjecture (1955) was proved by Lovász (1978) using the Borsuk-Ulam theorem; all subsequent proofs, extensions
and generalizations also relied on Algebraic Topology results, namely the Borsuk-Ulam theorem and its extensions. Only in
2000, Matoušek provided the first combinatorial proof of the Kneser conjecture. Here we provide a hypergraph coloring theorem,
with a combinatorial proof, which has as special cases the Kneser conjecture as well as its extensions and generalization
by (hyper)graph coloring theorems of Dol’nikov, Alon-Frankl-Lovász, Sarkaria, and Kriz. We also give a combinatorial proof
of Schrijver’s theorem.
Oblatum 17-IV-2001 & 12-IX-2001?Published online: 19 November 2001
An erratum to this article is available at . 相似文献
10.
We provide a new analytical proof for a strengthened version of the variable radius form of the union of closed balls conjecture. We also introduce a strong version of this conjecture and discuss its validity. 相似文献
11.
Bianca Satco 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):260-269
The aim of this paper is to obtain an existence result for impulsive differential inclusions of first order with boundary conditions in Hilbert spaces under a hypothesis of integrability in the Henstock-Lebesgue sense for the multifunction on the right-hand side. The proof is based on the assumption that there exists a solution tube for the inclusion taken under consideration (this novel concept which generalizes the extensively used notions of upper and lower solution was adapted to the present setting). Finally, a compactness property is proved. 相似文献
12.
We provide a new proof of the Wong-Rosay theorem, using the structure of the ring of holomorphic functions. As a byproduct, we provide an analogous theorem for classical bounded symmetric domains. The second main result of this article concerns a new existence theorem for holomorphic peaking functions at a hyperbolic orbit accumulation boundary point. Finally, we give a proof of a version of the Greene-Krantz conjecture using holomorphic vector fields and a strengthened Hopf lemma. 相似文献
13.
Serge Bouc 《Mathematische Zeitschrift》2013,274(1-2):367-372
In this note, I propose the following conjecture: a finite group $G$ is nilpotent if and only if its largest quotient $B$ -group $\beta (G)$ is nilpotent. I give a proof of this conjecture under the additional assumption that $G$ be solvable. I also show that this conjecture is equivalent to the following: the kernel of restrictions to nilpotent subgroups is a biset-subfunctor of the Burnside functor. 相似文献
14.
Thomas C. Hales John Harrison Sean McLaughlin Tobias Nipkow Steven Obua Roland Zumkeller 《Discrete and Computational Geometry》2010,44(1):1-34
The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater
than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and complex.
The process of revision and review did not end with the publication of the proof. This article summarizes the current status
of a long-term initiative to reorganize the original proof into a more transparent form and to provide a greater level of
certification of the correctness of the computer code and other details of the proof. A final part of this article lists errata
in the original proof of the Kepler conjecture. 相似文献
15.
《Expositiones Mathematicae》2023,41(2):451-460
We give an elementary exposition of the little known work of Harold Davenport related to Hasse’s inequality. We formulate a new conjecture suggested by this proof that has implications for the classical Riemann hypothesis. 相似文献
16.
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting. 相似文献
17.
Nick Wright 《Journal of Functional Analysis》2005,220(2):265-303
The C0 coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space. In this paper we will prove the C0 version of the coarse Baum–Connes conjecture and show that K*(C*X0) is a topological invariant for a broad class of metric spaces. Using this result we construct a ‘geometric’ obstruction group to the coarse Baum–Connes conjecture for the bounded coarse structure. We then show under the assumption of finite asymptotic dimension that the obstructions vanish, and hence we obtain a new proof of the coarse Baum–Connes conjecture in this context. 相似文献
18.
Yuri G Zarhin 《Journal of Number Theory》2004,108(1):44-59
Recently, Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper, we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on properties of so-called polynomials of K3-type introduced by the author about 12 years ago. 相似文献
19.
S.L. Lee 《Linear algebra and its applications》1975,12(3):269-280
We give a proof of a conjecture of I.J. Schoenberg on B-splines for Cardinal Hermite interpolation without the assumption that the characteristics polynomial IIn,r(λ) is irreducible over the rational field. 相似文献
20.
Luis Dieulefait 《manuscripta mathematica》2012,139(1-2):71-89
In this article we give a proof of Serre’s conjecture for the case of odd level and arbitrary weight. Our proof does not use any modularity lifting theorem in characteristic 2 (moreover, we will not consider at all characteristic 2 representations at any step of our proof). The key tool in the proof is a very general modularity lifting result of Kisin, which is combined with the methods and results of previous articles on Serre’s conjecture by Khare, Wintenberger, and the author, and modularity results of Schoof for abelian varieties of small conductor. Assuming GRH, infinitely many cases of even level will also be proved. 相似文献