Copyright (c) 2009 Southern Illinois University Carbondale All rights reserved. http://opensiuc.lib.siu.edu/math_articles Recent documents in Articles and Preprints en-us Wed, 11 Nov 2009 23:22:58 PST 3600 http://opensiuc.lib.siu.edu/math_articles/105 http://opensiuc.lib.siu.edu/math_articles/105 Tue, 10 Nov 2009 16:23:19 PST An edge-magic total labelling (EMTL) of a graph G with n vertices and e edges is an injection λ:V(G) ∪ E(G)→[n+e], where, for every edge uv ∈ E(G), we have wtλ(uv)=kλ, the magic sum of λ. An edge-magic injection (EMI) μ of G is an injection μ : V(G) ∪ E(G) → N with magic sum kμ and largest label mμ. For a graph G we define and study the two parameters κ(G): the smallest kμ amongst all EMI's μ of G, and m(G): the smallest mμ amongst all EMI's μ of G. We find κ(G) for G ∈ G for many classes of graphs G. We present algorithms which compute the parameters κ(G) and m(G). These algorithms use a G-sequence: a sequence of integers on the vertices of G whose sum on edges is distinct. We find these parameters for all G with up to 7 vertices. We introduce the concept of a double-witness: an EMI μ of G for which both kμ=κ(G) and mμ=m(G) ; and present an algorithm to find all double-witnesses for G. The deficiency of G, def(G), is m(G)−n−e. Two new graphs on 6 vertices with def(G)=1 are presented. A previously studied parameter of G is κEMTL(G), the magic strength of G: the smallest kλ amongst all EMTL's λ of G. We relate κ(G) to κEMTL(G) for various G, and find a class of graphs B for which κEMTL(G)−κ(G) is a constant multiple of n−4 for G ∈B. We specialise to G=Kn, and find both κ(Kn) and m(Kn) for all n≤11. We relate κ(Kn) and m(Kn) to known functions of n, and give lower bounds for κ(Kn) and m(Kn). John P. McSorley http://opensiuc.lib.siu.edu/math_articles/104 http://opensiuc.lib.siu.edu/math_articles/104 Thu, 07 May 2009 12:59:43 PDT We prove five of Sun's conjectures on the index of the subgroup of fourth powers in the class group of binary quadratic forms. Robert W. Fitzgerald http://opensiuc.lib.siu.edu/math_articles/103 http://opensiuc.lib.siu.edu/math_articles/103 Thu, 12 Mar 2009 15:09:19 PDT In this paper we construct a Rankin-Selberg integral which represents the Spin10 X St L-function attached to the group GSO10 X PGL2. We use this integral representation to give some equivalent conditions for a generic cuspidal representation on GSO10 to be a functorial lift from the group G2 X PGL2. David Ginzburg http://opensiuc.lib.siu.edu/math_articles/102 http://opensiuc.lib.siu.edu/math_articles/102 Sat, 07 Mar 2009 16:07:13 PST In this paper we provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of "almost orthogonal" representations, that is representations τ with the property that the symmetric square L-function, twisted by some Hecke character ω has a pole. Our theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) GSpin2n to GL2n. Joseph Hundley http://opensiuc.lib.siu.edu/math_articles/101 http://opensiuc.lib.siu.edu/math_articles/101 Sat, 07 Mar 2009 16:05:02 PST In this paper we provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of "almost symplectic" representations, that is representations τ with the property that the exterior square L-function twisted by some Hecke character ω has a pole. Our theory supplements the recent work of Asgari-Shahidi on the functorial lift from GSpin2n+1 groups to GL2n. Joseph Hundley http://opensiuc.lib.siu.edu/math_articles/100 http://opensiuc.lib.siu.edu/math_articles/100 Sat, 07 Mar 2009 16:01:52 PST We describe two new Eulerian Rankin-Selberg integrals, using the same Eisenstein series defined on the group E8, and cuspidal representations from GL5 and GSpin11, respectively. Connections with past work of Ginzburg, Bump-Ginzburg, Jiang-Rallis and others are described. We give some details of how to relate our two integrals via formal manipulations. David Ginzburg http://opensiuc.lib.siu.edu/math_articles/99 http://opensiuc.lib.siu.edu/math_articles/99 Sat, 07 Mar 2009 15:55:36 PST We show a relation between a certain period and the existence of a simple pole for the spin and standard partial L functions corresponding to a generic cuspidal representation defined on the group GSO8(A). We also relate these two conditions with the functorial lift from the exceptional group G2 to GSO8. The main new ingridient is a new multivariable Rankin-Selberg integral which represents the above two L functions. David Ginzburg http://opensiuc.lib.siu.edu/math_articles/98 http://opensiuc.lib.siu.edu/math_articles/98 Sat, 07 Mar 2009 15:53:26 PST In this paper we provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially symplectic representations, that is representations τ with the property that the exterior square L-function twisted by some Hecke character ω has a pole at s = 1. Our theory supplements the recent work of Asgari-Shahidi on the functorial lift from the general Spin groups GSpin2n+1 to GL2n. Joseph Hundley http://opensiuc.lib.siu.edu/math_articles/97 http://opensiuc.lib.siu.edu/math_articles/97 Sat, 07 Mar 2009 15:45:14 PST Joseph Hundley http://opensiuc.lib.siu.edu/math_articles/96 http://opensiuc.lib.siu.edu/math_articles/96 Sat, 07 Mar 2009 14:46:03 PST Two multi-variable Rankin-Selberg integrals are studied. They may be regarded as extending the theory begun in [G-H1]. Each is shown to be Eulerian with the unramified contribution given explicitly in terms of partial Langlands L-functions. Joseph Hundley