Let φ be a Drinfeld module of rank 2 over the field of rational functions F = Fq(T ), with EndF̄ (φ) = Fq[T ]. Let K be a fixed imaginary quadratic field over F and d a positive integer. For each prime p of good reduction for φ, let πp(φ) be a root of the characteristic polynomial of the Frobenius endomorphism of φ over the finite field Fq[T ]/p. Let Πφ(K; d) be the number of primes p of degree ...

Motivated by the question of when the characteristic polynomial of a matroid factorizes, we study join-factorizations of broken circuit complexes and rooted complexes (a more general class of complexes). Such factorizations of complexes induce factorizations not only of characteristic polynomial but also of the Orlik-Solomon algebra of the matroid. The broken circuit complex of a matroid factor...

Let T be a self-affine tile that is generated by an expanding integral matrix A and a digit set D. It is known that many properties of T are invariant under the Z-similarity of the matrix A. In [LW1] Lagarias and Wang showed that if A is a 2 × 2 expanding matrix with |det(A)| = 2, then the Z-similar class is uniquely determined by the characteristic polynomial of A. This is not true if |det(A)|...

We give a formula for the number of rational points of projective algebraic curves de ned over a nite eld, and a bound \ a la Weil" for connected ones. More precisely, we give the characteristic polynomials of the Frobenius endomorphism on the etale `-adic cohomology groups of the curve. Finally, as an analogue of Artin's holomorphy conjecture, we prove that, if Y ! X is a nite at morphism betw...

We investigate the joint moments of the 2k-th power of the characteristic polynomial of random unitary matrices with the 2h-th power of the derivative of this same polynomial. We prove that for a fixed h, the moments are given by rational functions of k, up to a well-known factor that already arises when h = 0. We fully describe the denominator in those rational functions (this had already been...

Abstract: Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are related to certain configurations of vicious random walkers and to the enumeration of plane partitions. The combinatorial meaning of the average of the c...

We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension n. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension p. The developed method leads to the following result: for this conditional measure, writing Z (p) U for the first nonzero derivative of the characteristic polyn...

and the asymptotic behaviour of its solutions. We prove that the existence and uniqueness of solutions depend mainly on the coefficients c , i s 1, 2, . . . , and on i the smoothness of functions in the solution space. As far as the asymptotic behaviour of analytic solutions is concerned, the c have little effect. We prove that i Ž . if Re a ) 0 then the solution y t either grows exponentially ...

For an abelian group , a formula to compute the characteristic polynomial of a -graph has been obtained by Lee and Kim [Characteristic polynomials of graphs having a semi-free action, Linear algebra Appl. 307 (2005) 35–46]. As a continuation of this work, we give a computational formula for generalized characteristic polynomial of a -graph when is a finite group. Moreover, after showing that th...

In this paper, we evaluate the stability margin of a Fiat Dedra engine model to explore possible applications of theoretical achievements in the parametric approach to robust control problems. The study is based on two versions of the model with uncertainties. One is the original model, which has a multilinear characteristic polynomial, while the other is an affine-linearized model which is obt...