共查询到20条相似文献,搜索用时 171 毫秒
1.
The paper gives bounds for the approximation of the values of Ramanujan's Mock Theta functions of third order and more generally of some q-hypergeometric functions by the elements of an algebraic number field. Simultaneous approximations for the values of q-exponential function are also obtained. All the results are given both in the archimedean and p-adic case. 相似文献
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We prove the one-, two-, and three-variable Iwasawa-Greenberg Main Conjectures for a large class of modular forms that are ordinary with respect to an odd prime p. The method of proof involves an analysis of an Eisenstein ideal for ordinary Hida families for GU(2,2). 相似文献
4.
We consider George Andrews’ fundamental theorem on partitions with initial repetitions and obtain some partition identities and parity results. A simplified, diagram-free, version of William Keith’s bijective proof of the theorem is presented. Lastly, we obtain extensions and variations of the theorem using a class of Rogers–Ramanujan-type identities for n-color partitions studied by A.K. Agarwal. 相似文献
5.
Bud Coulson Shashank Kanade James Lepowsky Robert McRae Fei Qi Matthew C. Russell Christopher Sadowski 《The Ramanujan Journal》2017,42(1):97-129
We present what we call a “motivated proof” of the Göllnitz–Gordon–Andrews identities. A similar motivated proof of the Rogers–Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon’s identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the Göllnitz–Gordon–Andrews identities will illuminate certain twisted vertex-algebraic constructions. 相似文献
6.
S. F. Keating 《Proceedings of the American Mathematical Society》2002,130(11):3433-3437
Theta functions have historically played a prominent role in number theory. One such role is the construction of modular forms. In this work, a generalized theta function is used to construct an infinite family of summation identities. Our results grew out of some observations noted during a presentation given by the author at the 1992 AMS-MAA-SIAM Joint Meetings in Baltimore.
7.
Summary We provide an alternate proof of McMullen's theorem on contractive properties of the Poincaré series operator in the special case of the universal covering. This case includes in particular Kra's Theta Conjecture.Oblatum 16-X-1991 & 14-IV-1992First author supported in part by a grant from the National Science Foundation 相似文献
8.
《Journal of Combinatorial Theory, Series B》1987,43(2):223-240
Perfect Graphs were defined by Claude Berge in 1961. Since that time this class of graphs has been intensely studied. Much of the work has been directed towards proving Berge's Strong and Weak Perfect Graph Conjectures. L. Lovász finally demonstrated the Weak Perfect Graph Conjecture in 1972. Vaśek Chvátal, in 1982, proposed the Semi-Strong Perfect Graph Conjecture which falls between these two conjectures. This conjecture suggests that the perfection of a graph depends solely on the way that the chordless paths with three edges are distributed within the graph. This paper contains a proof of Chvátal's conjecture. 相似文献
9.
Alexei N. Skorobogatov 《Israel Journal of Mathematics》1992,80(3):359-379
We estimate exponential sums with additive character along an affine variety given by a system of homogeneous equations, with
a homogeneous function in the exponent. The proof uses the results of Deligne’s Weil Conjectures II and a generalization of
Lefschetz hyperplane theorem to singular varieties. We apply our estimate to obtain an upperbound for the number of integer
solutions of a system of homogeneous equations in a box. Another application is devoted to uniform distribution of solutions
of a system of homogeneous congruences modulo a prime in the following sense: the portion of solutions in a box is proportional
to the volume of the box, provided the box is not very small. 相似文献
10.
Somjit Dutt 《Journal of Number Theory》2011,131(9):1547-1552
We prove two identities involving Dirichlet series, in the denominators of whose terms sums of two, three and four squares appear. These follow from two classical identities of Jacobi involving the four Jacobian Theta Functions θ1(z;q), θ2(z;q), θ3(z;q) and θ4(z;q), by the application of the Mellin transform. These results motivate the well-known correspondence between the set of the four Jacobian Theta Functions and the set of four classical zeta functions of which the Riemann Zeta Function is the third, and the Dirichlet Beta Function is the first. 相似文献
11.
D. A. Rumynin 《Siberian Mathematical Journal》2013,54(5):905-921
We study the algebras that are defined by identities in the symmetric monoidal categories; in particular, the Lie algebras. Some examples of these algebras appear in studying the knot invariants and the Rozansky-Witten invariants. The main result is the proof of the Westbury conjecture for a K3-surface: there exists a homomorphism from a universal simple Vogel algebra into a Lie algebra that describes the Rozansky-Witten invariants of a K3-surface. We construct a language that is necessary for discussing and solving this problem, and we formulate nine new problems. 相似文献
12.
Behrndt Jussi; Malamud Mark M.; Neidhardt Hagen 《Proceedings London Mathematical Society》2008,97(3):568-598
For a scattering system {A, A0} consisting of self-adjoint extensionsA and A0 of a symmetric operator A with finite deficiency indices,the scattering matrix {S()} and a spectral shift function arecalculated in terms of the Weyl function associated with a boundarytriplet for A*, and a simple proof of the Krein–Birmanformula is given. The results are applied to singular Sturm–Liouvilleoperators with scalar and matrix potentials, to Dirac operatorsand to Schrödinger operators with point interactions. 相似文献
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D.M. Bressoud 《Journal of Number Theory》1983,16(2):235-241
A proof of the Rogers-Ramanujan identities is presented which is brief, elementary, and well motivated; the “easy” proof of whose existence Hardy and Wright had despaired. A multisum generalization of the Rogers-Ramanujan identities is shown to be a simple consequence of this proof. 相似文献
15.
Cristian D. Popescu 《Compositio Mathematica》1999,118(3):263-290
Based on results obtained in [15], we construct groups of special S-units for function fields of characteristic p>0, and show that they satisfy Gras-type Conjectures. We use these results in order to give a new proof of Chinburg's 3-Conjecture on the Galois module structure of the group of S-units, for cyclic extensions of prime degree of function fields. 相似文献
16.
In this note we investigate the solutions of a class of difference equations and prove that Conjectures 4.8.2, 4.8.3, 5.4.6 and 6.10.3 proposed by M. Kulenovic and G. Ladas in [M. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, Chapman & Hall/CRC Press, 2002] are true. 相似文献
17.
M. A. Vsemirnov 《Journal of Mathematical Sciences》1999,96(5):3486-3492
A new proof of the combinatorial Macdonald identities is presented. It is shown that one may regard these identities as a decomposition of certain multidimensional theta-functions into infinite products. The proof is based on some analytical properties of theta-functions. It is briefly discussed how one can modify the proof in order to replace analytical arguments by formal ones involving only operations with formal series.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 67–77.The author is grateful to A. M. Vershik and Yu. M. Bazlov for their interest and helpful comments.This research was supported by ISSEP (grant No. A96-1965). 相似文献
18.
S. Yu. Nemirovskii 《Mathematical Notes》1996,60(3):306-312
In the paper, we consider applications of strictly pseudoconvex domains to the problems of algebraicity and rationality. We
give a new proof of the Kodaira theorem on the algebraicity of a surface and we also prove a multidimensional version of this
theorem. Theorems analogous to the Hodge index theorem and the Lefschetz theorem about (1, 1)-classes are obtained for strictly
pseudoconvex domains. Conjectures on the geometry of strictly pseudoconvex domains on algebraic surfaces are formulated.
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 414–422, September, 1996.
This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00225 and by the International
Science Foundation under grant No. 508. 相似文献
19.
Ivica Martinjak 《Periodica Mathematica Hungarica》2017,75(2):244-254
We present a family of identities including both binomial coefficients and a power of a natural number \(m \ge 2\). We find a combinatorial interpretation of these identities, which provides bijective proof. Dual alternating sign identities are also presented. 相似文献
20.
We give a short combinatorial proof of the Euler relation for convex polytopes in the context of oriented matroids. Using counting arguments we derive from the Euler relation several identities holding in the lattice of flats of an oriented matroid. These identities are proven for any matroid by Möbius inversion. 相似文献