Related papers: Simple zeros of automorphic $L$-functions

We give a proof of the existence of Asai, exterior square, and symmetric square local $L$-functions, $\gamma$-factors and root numbers in characteristic $p$, including the case of $p = 2$. Our study is made possible by developing the…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…

Let $f:S^2\to \mathbb{R}$ be a Morse function on the $2$-sphere and $K$ be a connected component of some level set of $f$ containing at least one saddle critical point. Then $K$ is a $1$-dimensional CW-complex cellularly embedded into…

We extend some results of Gun, Murty, and Rath on elliptic modular forms. We take ANY Fuchsian triangle group with a cusp and look at power series expansions in a natural parameter around that cusp. Consider the automorphic forms for such a…

Answering a question of Browkin, we provide a new unconditional proof that the Dedekind zeta function of a number field $L$ has infinitely many nontrivial zeros of multiplicity at least 2 if $L$ has a subfield $K$ for which $L/K$ is a…

We study the restriction of the Bump-Friedberg integrals to affine lines $\{(s+\alpha,2s),s\in\C\}$. It has a simple theory, very close to that of the Asai $L$-function. It is an integral representation of the product…

We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion…

I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level $G(Z-hat)$ and various small weights for an example of a rank 3 unitary…

We show that smooth well formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.

Let $G$ be a connected reductive group over a finite field $\mathfrak{f}$ of order $q$. When $q$ is small, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak{f})$ admits irreducible, cuspidal representations…

We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism…

Let $\mathfrak{F}_n$ be the set of all cuspidal automorphic representations $\pi$ of $\mathrm{GL}_n$ over a number field with unitary central character. We prove two unconditional large sieve inequalities for the Hecke eigenvalues of…

Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and…

It is shown that the Lie algebra of the automorphic, meromorphic sl(2, C) -valued functions on a torus is a geometric realization of a certain infinite-dimensional finitely generated Lie algebra. In the trigonometric limit, when the modular…

In this paper we prove the following theorem. Let L/\Q_p be a finite extension with ring of integers O_L and maximal ideal lambda. Theorem 1. Suppose that p >= 5. Suppose also that \rho:G_\Q -> GL_2(O_L) is a continuous representation…

Let pi be a cuspidal, automorphic representation of GSp(4) attached to a Siegel modular form of degree 2. We refine the method of Furusawa to obtain an integral representation for the degree-8 L-function L(s,pi x tau), where tau runs…

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…

The L-function $ L(\rho_\lambda, s) $ of an almost everywhere unramified $ \lambda $-adic representation $ \rho_\lambda $ of a global function field $ \mathbb{F}_q(C) $ is known to be a rational function in $ q^{-s} $ satisfying a…

We give a detailed description of the algebraic group Aut(g) of automorphisms of a simple finite dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0. We also give a description of the group of…

We apply results proved in [Li19] to the linear order expansions of non-trivial free homogeneous structures and the universal n-linear order for $n\geq 2$, and prove the simplicity of their automorphism groups.