𝔖 Bobbio Scriptorium
✦   LIBER   ✦

k-Hypermonogenic automorphic forms

✍ Scribed by D. Constales; R.S. Kraußhar; John Ryan

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
196 KB
Volume
126
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

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-vanishing monogenic automorphic form a Clifford algebra valued Maaß wave form. In the second part of the paper we compute the Fourier expansion of the k-hypermonogenic Eisenstein series which provide us with the simplest non-vanishing examples of k-hypermonogenic automorphic forms.

📜 SIMILAR VOLUMES

Closed Geodesics and Periods of Automorp
Closed Geodesics and Periods of Automorphic Forms
✍ Richard Sharp 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 146 KB

We study the detailed structure of the distribution of Eichler Shimura periods of an automorphic form on a compact hyperbolic surface. We show that these periods do not cluster around the asymptotic period over a homology class discovered by Zelditch. 2001 Academic Press ## 0. INTRODUCTION AND RES

Automorphic Forms and Sums of Squares ov
Automorphic Forms and Sums of Squares over Function Fields
✍ Jeffrey Hoffstein; Kathy D. Merrill; Lynne H. Walling 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 206 KB

We develop some of the theory of automorphic forms in the function field setting. As an application, we find formulas for the number of ways a polynomial over a finite field can be written as a sum of k squares, k 2. As a consequence, we show every polynomial can be written as a sum of 4 squares. We

Automorphic Forms, Fake Monster Algebras
Automorphic Forms, Fake Monster Algebras, and Hyperbolic Reflection Groups
✍ Nils R. Scheithauer 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 170 KB

We construct two families of automorphic forms related to twisted fake monster algebras and calculate their Fourier expansions. This gives a new proof of their denominator identities and shows that they define automorphic forms of singular weight. We also obtain new infinite product identities which