Topics in Automorphic Forms
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A brief overview of modular and automorphic forms
These notes were originally written in Fall 2010 to provide a very quick overview of some basic topics in modular forms, automorphic forms and automorphic representations. I have not made any significant changes since, or even proofread them completely (so some information may be outdated, and errors may remain), mostly just corrected some typos. If you spy any more errors, or have suggestions,...
متن کاملk-hypermonogenic automorphic forms
In this paper we deal with monogenic and k-hypermonogenic automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic forms are exactly the 0-hypermonogenic automorphic forms. In the first part we establish an explicit relation between k-hypermonogenic automorphic forms and Maaß wave forms. In particular, we show how one can construct from any arbitrary non-vani...
متن کاملOrthogonality relations for k-hypermonogenic automorphic forms
In this paper we deal with monogenic and k-hypermonogenic automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic forms are exactly the 0-hypermonogenic automorphic forms. In the first part we establish an explicit relation to Maaß wave forms. In the second part we introduce Clifford algebra valued k-hypermonogenic cusp forms. We construct k-hypermonogenic P...
متن کاملPOINCARÉ SERIES AND MODULAR FUNCTIONS FOR U(n, 1)
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...
متن کاملExplicit Calculations of Automorphic Forms for Definite Unitary Groups
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(Ẑ) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic f...
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