相关论文: Poles of unramified degenerate Eisenstein series

Let $G$ be a linear split algebraic group. The degenerate Eisenstein series associated to a maximal parabolic subgroup $E_{P}(f^{0},s,g)$ with the spherical section $f^{0}$ is studied in the first part of the thesis. In this part, we study…

I this paper we determine poles in the right--half plane and images of degenerate Eisenstein series for $GL_n(\Bbb A_\mathbb Q)$ induced from a character on a maximal parabolic subgroup. We apply those results to determine poles of…

We determine the poles of the Eisenstein series on a general linear group, induced from two Speh representations, $\Delta(\tau,m_1)|\cdot|^s\times\Delta(\tau,m_2)|\cdot|^{-s}$, $Re(s)\geq 0$, where $\tau$ is an irreducible, unitary,…

In this paper we obtain a complete description of images and poles of degenerate Eisenstein series attached to maximal parabolic subgroups of $Sp_4(\mathbb A)$, where $\mathbb A$ is the ring of adeles of $\mathbb Q$.

We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

The cancellations of poles of degenerate Eisenstein series were studied by Hanzer and Mui\'{c}. This paper generalizes the method and the result to Eisenstein series constructed from inducing two Speh representations…

In this paper, we study the reducibility of degenerate principal series of the simple, simply-connected exceptional group of type $E_8$. Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these…

In this paper, we study the degenerate principal series of a split, simply-connected, simple p-adic group of type $E_7$. We determine the points of reducibility and the maximal semi-simple subrepresentation at each point.

In this paper, we study the reducibility of degenerate principal series of the simple, simply-connected exceptional group of type $E_6$. Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these…

This manuscript has two goals: 1. To write an explicit description of the degenerate residual spectrum of the split, simple, simply-connected, exceptional groups of type $E_n$ (for $n=6,7,8$). 2. To set a practical guide for similar…

If E(z,s) is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z,s) has a "Siegel zero." That is E(z,\beta)=0 for a real number \beta just to the left of one. We give a generalization of this…

We consider the residues at the poles in the right half plane of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit,…

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,…

We construct \'etale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic fields that admit everywhere unramified generalized…

We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…

We prove linear independence of indefinite iterated Eisenstein integrals over the fraction field of the ring of formal power series $\mathbb{Z}[[q]]$. Our proof relies on a general criterium for linear independence of iterated integrals,…

For a split reductive group ${}^L G$ over a global field, we determine the spectrum of the spherical Hecke algebra coming from the unramified Eisenstein series for the minimal parabolic ${}^L B$. This is done using a certain decomposition…

We determine the unipotent orbits attached to degenerate Eisenstein series on general linear groups. This confirms a conjecture of David Ginzburg. This also shows that any unipotent orbit of general linear groups does occur as the unipotent…

This paper provides a simple method to extract the zeros of some weight two Eisenstein series of level $N$ where $N=2,3,5$ and $7$. The method is based on the observation that these Eisenstein series are integral over the graded algebra of…

Using the action of the Galois group of a normal extension of number fields, we generalize and symmetrize various fundamental statements in algebra and algebraic number theory concerning splitting types of prime ideals, factorization types…