oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
On ground fields of arithmetic hyperbolic reflection groups  [PDF]
Viacheslav V. Nikulin
Mathematics , 2007,
Abstract: Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing ground fields of arithmetic hyperbolic reflection groups are defined, and good bounds of their degrees (over Q) are obtained. For example, degree of the ground field of any arithmetic hyperbolic reflection group in dimension at least 6 is bounded by 56. These results could be important for further classification. We also formulate a mirror symmetric conjecture to finiteness of the number of arithmetic hyperbolic reflection groups which was established in full generality recently.
On ground fields of arithmetic hyperbolic reflection groups. III  [PDF]
Viacheslav V. Nikulin
Mathematics , 2007, DOI: 10.1112/jlms/jdp003
Abstract: This paper continues arXiv.org:math.AG/0609256, arXiv:0708.3991 and arXiv:0710.0162 . Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimension at least 3 are defined, and explicit bounds of their degrees (over Q) are obtained. Thus, now, explicit bound of degree of ground fields of arithmetic hyperbolic reflection groups is known in all dimensions. Thus, now, we can, in principle, obtain effective finite classification of arithmetic hyperbolic reflection groups in all dimensions together.
The transition constant for arithmetic hyperbolic reflection groups  [PDF]
Viacheslav V. Nikulin
Mathematics , 2009,
Abstract: The transition constant was introduced in our 1981 paper and denoted as N(14). It is equal to the maximal degree of the ground fields of V-arithmetic connected edge graphs with 4 vertices and of the minimality 14. This constant is fundamental since if the degree of the ground field of an arithmetic hyperbolic reflection group is greater than N(14), then the field comes from very special plane reflection groups. In our recent paper (see also arXiv:0708.3991), we claimed its upper bound 56. Using similar but more difficult considerations, here we improve this bound. These results could be important for further classification.
Arithmetic hyperbolic reflection groups  [PDF]
Mikhail Belolipetsky
Mathematics , 2015,
Abstract: This is a survey article about arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.
Finiteness of arithmetic hyperbolic reflection groups  [PDF]
Ian Agol,Mikhail Belolipetsky,Peter Storm,Kevin Whyte
Mathematics , 2006,
Abstract: We prove that there are only finitely many conjugacy classes of arithmetic maximal hyperbolic reflection groups.
On fields of definition of arithmetic Kleinian reflection groups II  [PDF]
Mikhail Belolipetsky,Benjamin Linowitz
Mathematics , 2012,
Abstract: Following the previous work of Nikulin and Agol, Belolipetsky, Storm, and Whyte it is known that there exist only finitely many (totally real) number fields that can serve as fields of definition of arithmetic hyperbolic reflection groups. We prove a new bound on the degree $n_k$ of these fields in dimension 3: $n_k$ does not exceed 9. Combined with previous results of Maclachlan and Nikulin, this leads to a new bound $n_k \le 25$ which is valid for all dimensions. We also obtain upper bounds for the discriminants of these fields and give some heuristic results which may be useful for the classification of arithmetic hyperbolic reflection groups.
On fields of definition of arithmetic Kleinian reflection groups  [PDF]
Mikhail Belolipetsky
Mathematics , 2007,
Abstract: We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.
Computing arithmetic invariants for hyperbolic reflection groups  [PDF]
Omar Antolin-Camarena,Gregory R. Maloney,Roland K. W. Roeder
Mathematics , 2007,
Abstract: We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in $\mathbb{H}^3$, the commensurability invariants known as the invariant trace field and invariant quaternion algebra. Our scripts also allow one to determine arithmeticity of such groups and the isomorphism class of the invariant quaternion algebra by analyzing its ramification. We present many computed examples of these invariants. This is enough to show that most of the groups that we consider are pairwise incommensurable. For pairs of groups with identical invariants, not all is lost: when both groups are arithmetic, having identical invariants guarantees commensurability. We discover many ``unexpected'' commensurable pairs this way. We also present a non-arithmetic pair with identical invariants for which we cannot determine commensurability.
Evaluation of Electromagnetic Fields Due to Inclined Lightning Channel in Presence of Ground Reflection
Mahdi Izadi;Mohd Zainal Abidin Ab Kadir;Maryam Hajikhani
PIER , 2013, DOI: 10.2528/PIER12112503
Abstract: In this paper, analytical field expressions are proposed to determine the electromagnetic fields due to an inclined lightning channel in the presence of a ground reflection at the striking point. The proposed method can support different current functions and models directly in the time domain without the need to apply any extra conversions. A set of measured electromagnetic fields associated with an inclined lightning channel from a triggered lightning experiment is used to evaluate the proposed field expressions. The results indicate that the peak of the electromagnetic fields is dependent on the channel angle, the observation point angle as well as the value of the ground reflection factor due to the difference between channel and ground impedances. Likewise, the effect of the channel parameters and the ground reflection on the values of the electromagnetic fields is considered and the results are discussed accordingly.
Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups  [PDF]
Viacheslav V. Nikulin
Mathematics , 2008,
Abstract: An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces over C with reflective Picard lattices can be characterized in terms of compositions of their self-correspondences via moduli of sheaves with primitive isotropic Mukai vector: Their self-correspondences with integral action on the Picard lattice are numerically equivalent to compositions of a finite number of especially simple self-correspondences via moduli of sheaves. This relates two topics: Self-correspondences of K3 surfaces via moduli of sheaves and Arithmetic hyperbolic reflection groups. It also raises several natural unsolved related problems.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.