Related papers: A Spiegelungssatz for function field $L$-series

In a recent paper, Castella and Hsieh proved results for Selmer groups associated with Galois representations attached to newforms twisted by Hecke characters of an imaginary quadratic field. These results are obtained under the so-called…

We introduce a type of graph integrals on elliptic curves from the heat kernel. We show that such graph integrals have modular properties under the modular group $SL(2, \Z)$, and prove the polynomial nature of the anti-holomorphic…

We first construct a dynamical systems model which in its steady-state serves as an analytic continuation of the completed Riemann zeta function over the entire critical strip. The resulting mathematical construct involves a linear…

Let $R$ be a commutative noetherian ring, and let $\mathscr{S}$(resp. $\mathscr{L}$) be a Serre(resp. localizing) subcategory of the category of $R$-modules. If $\Bbb F$ is an unbounded complex of $R$-modules Tor-perpendicular to…

Let k be a field, let R be a ring of polynomials in a finite number of variables over k, let D be the ring of k-linear differential operators of R and let f be a non-zero element of R. It is well-known that R_f, with its natural D-module…

We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a reductive algebraic group G defined and split over a non-archimedean local field K. Following their lines, we prove that the generalized Steinberg representations of G…

We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an…

Basic properties of symplectic reflection algebras over an algebraically closed field k of positive characteristic are laid out. These algebras are always finite modules over their centres, in contrast to the situation in characteristic 0.…

We classify quadratic SL(2,K)- and sl(2,K)-modules by crude computation, generalizing in the first case a Theorem proved independently by F.-G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearization results…

We prove that, e.g., if mu >cf(mu)= aleph_0 and mu>2^{aleph_0} and every stationary family of countable subsets of mu^+ reflect in some subset of mu^+ of cardinality aleph_1, then the SCH for mu^+ (moreover, for mu^+, any scale for mu^+ has…

We establish a Siegel-Weil formula for classical groups over a function field with odd characteristic, which asserts in many cases that the Siegel Eisenstein series is equal to an integral of a theta function. This is a function-field…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

We introduce a generalization of stationary set reflection which we call "filter reflection", and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection…

We introduce a general version of singular compactness theorem which makes it possible to show that being a $\Sigma$-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed…

To every abelian subvariety of a principally polarized abelian variety $(A, \mathcal{L})$ we canonically associate a numerical class in the N\'eron-Severi group of $A$. We prove that these classes are characterized by their intersection…

Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical…

The notion of multiplicity of a module first arose as consequence of Hilbert's work on commutative algebra, relating the dimension of rings with the degree of certain polynomials. For noncommutative rings, the notion of multiplicity first…

We show that the central value of class group L-functions of CM fields can be expressed in terms of derivatives of real-analytic Hilbert Eisenstein series at CM points. Then, following an idea of Iwaniec and Kowalski we obtain a conditional…

We investigate the stabilization $\mathcal{S}$ of the module category over an artinian ring $\Lambda$ by formally inverting the tensor endofunctor given by the bimodule of relative noncommutative differential $1$-forms. It turns out that…

We introduce screw functions for Dirichlet series in the extended Selberg class. Then we prove that the Grand Riemann Hypothesis for a member of the extended Selberg class is equivalent to the nonpositivity of the corresponding screw…