Last edited by Voodooshicage

Monday, August 3, 2020 | History

5 edition of **Selberg Trace Formula for Psl** found in the catalog.

Selberg Trace Formula for Psl

Dennis A. Hejhal

- 154 Want to read
- 40 Currently reading

Published
**August 1983**
by Springer
.

Written in English

**Edition Notes**

Lecture Notes in Mathematics

The Physical Object | |
---|---|

Number of Pages | 806 |

ID Numbers | |

Open Library | OL7443209M |

ISBN 10 | 0387123237 |

ISBN 10 | 9780387123233 |

The Selberg zeta-function was introduced by Atle Selberg ().It is analogous to the famous Riemann zeta function = ∏ ∈ − −where is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the primes numbers. If is a subgroup of SL(2,R), the associated Selberg zeta function is defined as follows, = ∏ (− −) −. sides of the Selberg trace formula in our context, which will be used to prove Theorem 2. Dirac operator and Spin structure In this section, we deﬁne the Dirac operator over a coﬁnite quotient of PSL(2,R)byadiscrete subgroup. Equivalently, we consider the Lie .

We compute explicitly the Selberg trace formula for principal congruence subgroups of PGL(2, F q [t]) which is the modular group in positive characteristic also express the Selberg zeta function as a determinant of the Laplacian which is . The Arthur-Selberg trace formula is an equality between two kinds of traces; the geometric terms given by the conjugacy classes of a group and the spectral terms given by the induced representations. In general, these terms require a truncation in order to converge, which leads to .

A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general OF CONTENTS: 1. The Selberg trace formula for PSL(2,R) Vol 2. Book. Jan ; Dennis A. Hejhal; View. The continuous spectrum and Eisenstein-Maass series § 9. The Selberg trace formula (general case) § .

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During the last 10 years or so, mathematicians have become increasingly fascinated with the Selberg trace formula. These notes were written to help remedy this situation. Their main purpose is to provide a comprehensive development of the trace formula for PSL(2,R).

Volume one deals exclusively with the case of compact quotient space.1/5(2). Selberg Trace Formula for Psl (Lecture Notes in Mathematics) by Dennis A. Hejhal (Author) ISBN The Selberg Trace Formula for PSL (2,R) Volume 1. Authors: Hejhal, Dennis A. Free PreviewBrand: Springer-Verlag Berlin Heidelberg.

The Selberg Trace Formula for PSL(2,ℝ) Volume I. Authors; Dennis A. Hejhal; Search within book. Front Matter. PDF. The trace formula for compact Riemann surfaces Pages The trace formula for automorphic forms of weight m.

Dennis A. Hejhal. Pages The selberg trace formula for modular correspondences. Dennis A. Hejhal. The Selberg Trace Formula for PSL (2,R): Volume 2. This is a Print on Demand title. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc.

US$ US$ You save US$Author: Dennis A. Hejhal. The trace formula for compact Riemann surfaces.- The selberg zeta function.- The trace formula for vector-Valued functions.- The trace formula for automorphic forms of weight m.- The selberg trace formula for modular correspondences.

Series Title: Lecture notes in mathematics, Responsibility: Dennis A. Hejhal. The Selberg Trace Formula for PSL(2,ℝ) Volume 2. Authors; Dennis A. Hejhal; Search within book.

Front Matter. Pages I-VIII. PDF. Development of the trace formula (version A) Dennis A. Hejhal. Pages Version B of the selberg trace formula. Dennis A. Hejhal. Pages Version C of the selberg trace formula.

Dennis A. Hejhal. The Selberg trace formula for ${\rm PSL}_2({\bf R})^n$ About this Title. Isaac Y. Efrat. Publication: Memoirs of the American Mathematical Society.

Hejhal, The Selberg Trace Formula for PSL(2,R) - Volume I, p. 35 "Selberg noticed this similarity and was quickly led to a deeper study of trace formulas. Among other things, Selberg found that there is a zeta function which corresponds to [his trace formula] in the same way that [the Riemann zeta function] corresponds to [the Riemann-Weil explicit formula ].

formulas for its eigenvalues are known. In the case of more general quan-tum systems, the role of Selberg’s formula is taken over by the semiclassical Gutzwiller trace formula [11], [7]. We begin by reviewing the trace formulas for the simplest compact man-ifolds, the circle S1 (Section 1) and the sphere S2 (Section 2).

In both cases. The formula for the trace is given as $$ tr T_\phi = \sum\limits_{s in \Gamma} vol(\Gamma_\gamma \backslash G_\gamma) \int\limits_{G_\gamma \backslash G} \phi(g \gamma g^{-1}) \,d\,g.$$ The space $L^2(\Gamma\backslash G)$ decomposes of course into irreducible reps.

Additional Physical Format: Online version: Hejhal, Dennis A. Selberg trace formula for PSL (2, IR). Berlin ; New York: Springer-Verlag, The Selberg trace formula for Dirac operators Jens Bolte1 and Hans-Michael Stiepan2 Abteilung Theoretische Physik Universit¨at Ulm, Albert-Einstein-Allee 11 D Ulm, Germany Abstract We examine spectra of Dirac operatorson compact hyperbolicsurfaces.

Particular attention is devoted to symmetry considerations, leading to non-trivial. In Selberg [11], he introduced the trace formula and applied it to computations of traces of Hecke operators acting on the space of cusp forms of weight greater than or equal to two.

But for the case of weight one, the similar method is not effective. The Selberg Trace Formula and Related Topics About this Title. Dennis A. Hejhal, Peter Sarnak and Audrey Anne Terras, Editors. Publication: Contemporary Mathematics Publication Year Volume 53 ISBNs: (print); (online).

THE SELBERG TRACE FORMULA AND SELBERG ZETA-FUNCTION 5 Deﬁnition A representation χ∈ Rep(Γ,V) is singular6 at the cusp ζα of Γ iff the subspace Vα 6= {0}. If a cusp is not singular it is called regular.A representation χis called singular if it is singular at least at one cusp, and regular otherwise.

For each cusp ζα set kα = dimCVα,and k(Γ,χ) ≡. Here the trace formula is an extension of the Frobenius formula for the character of an induced representation of finite groups. When Γ is the cocompact subgroup Z of the real numbers G = R, the Selberg trace formula is essentially the Poisson summation formula.

He gives a reference to a book by Hilbert, but aside from the fact that I don't read German, it's not at all clear to me that this is the best place to learn from (in light of the fact that Hejhal's book is from and many books have been written since).

Buy psl Books at Shop amongst our popular books, including 8, Partially Supervised Learning, Partially Supervised Learning and more from psl. The Selberg Trace Formula For Psl (2,r): Volume 2. by Dennis A. Hejhal.

Paperback | July 1, $ online. $ list price. In stock online. Not available in stores. add to cart. Number theory, trace formulas, and discrete groups: symposium in honor of Atle Selberg, Oslo, Norway, JulyKarl Egil Aubert, Enrico Bombieri Academic Press, - Mathematics -.

Patterson S J The Selberg trace formula for PSL(2, R), Vol. 1, by Dennis A. Hejhal, Book review Bull. Am. Math. Soc. 84 Crossref Google Scholar [68].Access Google Sites with a free Google account (for personal use) or G Suite account (for business use).

In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 () –], it was proved that the Selberg zeta function for SL 2 (Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms.

The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg.