Let F be a number field and K a quadratic algebra over F , i.e., either F × F or a quadratic field extension of F . Denote by G the F -group defined by GL(2)/K. Then, given any cuspidal automorphic representation π of G(AF ), one has (cf. [8], [9]) a transfer to an isobaric automorphic representation Π of GL4(AF ) corresponding to the L-homomorphism LG → LGL(4). Usually, Π is called the Rankin-...

We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type ü(s) + 2Bu̇(s) + Au(s) = f(s) (∗), where A, B are densely defined closed linear operators acting in a Hilbert space H and f : R 7→ H is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions; every solution to (∗) ...

[1] Despite occasional contrary assertions in the literature, rewriting Eisenstein series, as opposed to more general automorphic forms, to make sense on adele groups is not about Strong Approximation. Strong Approximation does make precise the relation between general automorphic forms on adele groups and automorphic forms on SLn, but rewriting these Eisenstein series does not need this compar...

This paper is a continuation of [HT]. Let L be an imaginary CM field and let Π be a regular algebraic (i.e., Π∞ has the same infinitesimal character as an algebraic representation of the restriction of scalars from L to Q of GLn) cuspidal automorphic representation of GLn(AL) which is conjugate self-dual (Π ◦ c ∼= Π∨) and square integrable at some finite place. In [HT] it is explained how to at...

Abstract In this article, we improve our main results from [LL21] in two directions: First, allow ramified places the CM extension $E/F$ at which consider representations that are spherical with respect to a certain special maximal compact subgroup, by formulating and proving an analogue of Kudla–Rapoport conjecture for exotic smooth Rapoport–Zink spaces. Second, lift restriction on components ...

In the theory of automorphic forms, two classes of rank one reductive Lie groups O(n, 1) and U(n, 1) are the important objects. Automorphic forms on O(n, 1) have been intensively studied. In this paper we study the automorphic forms on U(n, 1). We construct infinitely many modular forms and non-holomorphic automorphic forms on U(n, 1) with respect to a discrete subgroup of infinite covolume. Mo...

We study almost automorphic (mild) solutions of the semilinear fractional equation ∂ t u = Au + ∂ α−1 t f(·, u), 1 < α < 2, considered in a Banach space X, where A is a linear operator of sectorial type ω < 0. We prove the existence and uniqueness of an almost automorphic mild solution assuming f(t, x) is almost automorphic in t for each x ∈ X, satisfies some Lipschitz type conditions and takes...

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We ...

A loop is automorphic if its inner mappings are automorphisms. Using socalled associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. Starting with suitable elements of an anisotropic plane in the vector space of 2 × 2 matrices over the field of prime order p, we construct a family of automorphic loops of order p with trivial center.