Jerome William Hoffman
Louisiana State University
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arXiv: Number Theory | 2012
Jerome William Hoffman; Ling Long; Helena A. Verrill
This paper is concerned with a compatible family of 4-dimensional l-adic representations ρl of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that: 1. It is automorphic: the L-function L(s,ρl∨) agrees with the L-function for an automorphic form for GL4(AQ), where ρl∨ is the dual of ρl. 2. For each prime p≥5 there is a basis hp = {hp+, hp-} of S3(Γ) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12. The key point is that the representation ρl admits a quaternion multiplication structure in the sense of Atkin, Li, Liu, and Long.
Transactions of the American Mathematical Society | 2006
Jerome William Hoffman; Hao Hao Wang
Let I = be a bigraded ideal in the bigraded polynomial ring k[s, u; t, v]. Assume that I has codimension 2. Then Z = V(I) C P 1 × P 1 is a finite set of points. We prove that if Z is a local complete intersection, then any syzygy of the f i vanishing at Z, and in a certain degree range, is in the module of Koszul syzygies. This is an analog of a recent result of Cox and Schenck (2003).
Journal of Algebra and Its Applications | 2007
Jerome William Hoffman; Haohao Wang
This paper is concerned with the relationships between two concepts, vanishing of cohomology groups and the structure of free resolutions. In particular, we study the connection between vanishing theorems for the local cohomology of multigraded modules and the structure of their free multigraded resolutions.
Transactions of the American Mathematical Society | 2000
Jerome William Hoffman; Steven H. Weintraub
Communications in Algebra | 1983
Jerome William Hoffman
Memoirs of the American Mathematical Society | 1984
Jerome William Hoffman
Advances in Mathematics | 2013
Jerome William Hoffman; Z. Liang; Yukiko Sakai; Xuezhi Zhao
Cahiers de Topologie et Géométrie Différentielle Catégoriques | 1996
Jerome William Hoffman
arXiv: Algebraic Geometry | 2014
Jerome William Hoffman; Dun Liang; Zhibin Liang; Ryotaro Okazaki; Yukiko Sakai; Haohao Wang
Libro de Resúmenes del XIII Encuentro de Álgebra Computacional y Aplicaciones: EACA 2012, 2012, ISBN 978-84-8138-770-4, págs. 115-118 | 2012
Jerome William Hoffman; Haohao Wang