In this paper we investigate the factorization behaviour of binomial polynomials (xn)=x(x−1)⋯(x−n+1)n! and their powers in ring integer-valued Int(Z). While it is well-known that are irreducible elements Int(Z), has not yet been fully understood. We fill gap show absolutely is, (xn)m factors uniquely into Int(Z) for all m∈N. By reformulating problem terms linear algebra number theory, question ...

The modular representation theory of the queer Lie superalgebra q(n) over characteristic p > 2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters χ and a criterion for the semisimplicity of the corresponding reduced enveloping algebras Uχ(q(n)). A (2p)-power divisibility of dimensions of q(n)-modules with nilpotent p-characters is estab...

In this paper, in honor of the memory of Serge Lang, we apply ideas of Chavdarov and work of Larsen to study the Qirreducibility, or lack thereof, of various orthogonal L-functions, especially L-functions of elliptic curves over function fields in one variable over finite fields. We also discuss two other approaches to these questions, based on work of Matthews, Vaserstein, and Weisfeller, and ...

This is an attempt to formulate a geometric Langlands conjecture for G = GSpin2n+1 and GSp2n, n ≥ 1. Namely, let Ǧ be the Langlands dual group (over Q̄l), let X be a smooth projective connected curve. Given a Ǧ-local system E on X , assuming some irreducibility type conditions on VE for some representations V of Ǧ, we propose a conjectural construction of a distinguished E-Hecke automorphic shea...

We describe a new general method to perform part of the setup stage of the XTR system introduced at Crypto 2000, namely finding the trace of a generator of the XTR group. Our method is substantially faster than the general method presented at Asiacrypt 2000. As a side result, we obtain an efficient method to test subgroup membership when

With any skew Young diagram one can associate a one parameter family of ”elementary” modules over the Yangian Y(glN ). Consider the twisted Yangian Y(gN ) ⊂ Y(glN ) associated with a classical matrix Lie algebra gN ⊂ glN . Regard the tensor product of elementary Yangian modules as a module over Y(gN ) by restriction. We prove its irreducibility for generic values of the parameters.

ACKNOWLEDGEMENTS The development of this thesis has been strongly influenced by two mentors. Accordingly, I thank Kalle Karu, who introduced me to log arc schemes, posed the irreducibility question to me, and suggested the log motivic integration problem and offered uncounted hours of discussion about it; and I thank Karen Smith, who has carefully read and commented on the many various drafts o...