相关论文: On Extending the Langlands-Shahidi Method to Arith…

In this paper, we prove the entirety of loop group Eisenstein series induced from cusp forms on the underlying finite dimensional group, by demonstrating their absolute convergence on the full complex plane. This is quite in contrast to the…

Based on Garland's work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms,…

We use mass formulas to construct minimal parabolic Eisenstein congruences for algebraic modular forms on reductive groups compact at infinity, and study when these yield congruences between cusp forms and Eisenstein series on the…

Let $G$ be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on $G$ induced from unramified cusp forms on finite-dimensional…

We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However…

Let $\Gamma$ be a geometrically finite Fuchsian group and suppose that $\chi\colon\Gamma\to\mathrm{GL}(V)$ is a finite-dimensional representation with non-expanding cusp monodromy. We show that the parabolic Eisenstein series for $\Gamma$…

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

Let $\pi$ traverse a sequence of cuspidal automorphic representations of GL(2) with large prime level, unramified central character and bounded infinity type. For G either of the groups GL(1) or PGL(2), let H(G) denote the assertion that…

We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig polynomials. As an application we compute Kazhdan-Lusztig polynomials which are needed to evaluate a character formula for reductive groups due to Lusztig. Some…

In this paper, we analyze the theta series associated to the quadratic form $Q(\mathbf{x}) := x_1^2 + x_2^2 + x_3^2 + x_4^2$ with congruence conditions on $x_i$ modulo $2, 3, 4$, and $6$. By employing special operators on modular,…

To every group of $I$-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the…

We calculate a $\mathrm{G}_2$-period of a Fourier coefficient of a cuspidal Eisenstein series on the split simply-connected group $\mathrm{E}_6$, and relate this period to the Ginzburg-Rallis period of cusp forms on $\mathrm{GL}_6$. This…

Let $G$ be a split group of type $F_4$ defined over a number field. We study the square-integrable automorphic representations of $G$ that can be realized as leading terms of degenerate Eisenstein series associated to various maximal…

We study certain types of Fuchsian groups of the first kind denoted by $R(N)$, which coincide with the Fricke groups or the arithmetic Hecke triangle groups of low levels. We find all elliptic points and cusps of $R(p)$ for a prime $p$, and…

We give a general identity relating Eisenstein series on general linear groups. We do it by constructing an Eisenstein series, attached to a maximal parabolic subgroup and a pair of representations, one cuspidal and the other a character,…

The geometric conjecture developed by the authors in [1,2,3,4] applies to the smooth dual Irr(G) of any reductive p-adic group G. It predicts a definite geometric structure - the structure of an extended quotient - for each component in the…

We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma<\text{Isom}(\mathbb{H}^{n+1})$, each full rank cusp corresponds to a cohomology class in…

We study the endomorphism algebras attached to Bernstein components of reductive $p$-adic groups and construct a local Langlands correspondence with the appropriate set of enhanced $L$-parameters, using certain "desiderata" properties for…

We study congruences between cuspidal modular forms and Eisenstein series at levels which are square-free integers and for equal even weights. This generalizes our previous results from Naskr\k{e}cki [17] for prime levels and provides…

In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properties of the prime ideals and their…