2 edition of **trace formula for Hecke operators over rank one lattices** found in the catalog.

trace formula for Hecke operators over rank one lattices

Werner Hoffmann

- 241 Want to read
- 23 Currently reading

Published
**1986**
by Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik in Berlin
.

Written in English

- Trade formulas.,
- Hecke operators.,
- Lattice theory.

**Edition Notes**

Statement | Werner Hoffmann ; communicated by H.G. Bothe. |

Series | Report / Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik,, R-Math-04/86, Report (Karl-Weierstrass-Institut für Mathematik) ;, R-Math-86/04. |

Classifications | |
---|---|

LC Classifications | QA243 .H64 1986 |

The Physical Object | |

Pagination | iv, 113 p. ; |

Number of Pages | 113 |

ID Numbers | |

Open Library | OL2426168M |

LC Control Number | 87112673 |

The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and ``fun'' subject in itself and abounds with an amazing number of surprising comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit › Books › New, Used & Rental Textbooks › Science & Mathematics. "The Selberg trace formula was originally introduced as an arithmetical relation, being a noncommutative generalisation of the Poisson summation formula, and it is used as such in number theory and harmonic the present context we view it as an identity relating dynamical quantitities, the quantal spectrum of the Laplace-Beltrami operator and the classical 'length spectrum' ~mwatkins/zeta/

Some Commentary on Atle Selberg’s Mathematics D. Hejhal and P. Sarnak series, combined with the general noncompact adelic trace formula developed by Arthur over many years, is among the most powerful tools that we have today in the theory of ture that, in the higher rank situation, much more is true; namely, that all lattices be inferred from the trace formula in higher rank. For example, it is well-known that the dimension of the space of automorphic forms with certain square-integrable Archimedean components can be computed using the trace formula ([Lan63]). More generally, there is an exact formula for traces of Hecke operators on automorphic forms whose

A prime geodesic theorem for higher rank spaces. Geometric and Functional Analy (). article preprint Panorama of zeta functions. in: Erich Kähler: Mathematical Works. de Gruyter book preprint A dynamical Lefschetz trace formula for algebraic Anosov diffeomorphisms. (with C. Deninger) One can see from this explicit formula that Hecke operators with different indices commute and that if a 0 = 0 then b 0 = 0, so the subspace S k of cusp forms of weight k is preserved by the Hecke operators. If a (non-zero) cusp form f is a simultaneous eigenform of all Hecke operators T m with eigenvalues λ m then a m = λ m a 1 and a 1 ≠ ://

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We derive the trace formula for Hecke operators acting in the completely G-decomposable subspace of L 2 (G Γ), where G is a real reductive Lie group and Γ is a lattice of rank one in Γ is arithmetic this means that G has Q-rank trace is given in terms of (weighted) orbital integrals and the usual intertwining and residual :// Trace formula for Hecke operators over rank one lattices.

Berlin: Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik, (OCoLC) Document Type: Book: All Authors / Contributors: Werner Hoffmann AbstractWe derive the trace formula for Hecke operators acting in the completely G-decomposable subspace of L2(GΓ), where G is a real reductive Lie group and Γ is a lattice of rank one in G.

If Γ is arithmetic this means that G has Q-rank :// The Trace Formula and Hecke Operators 21 We shall have to be content to say only a few words about the terms in () and ().

In each case, M is summed over Levi components of standard parabolic subgroups P of G, and |ch(a M)| denotes the number of chambers in the vector space a.M. In (), {M(Q)} stands for the conjugacy classes in Af(Q). Abstract. Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ℝ).

In this situation, we prove an invariant form of the Selberg trace formula for Hecke :// Traces of Hecke Operators 1. Introduction 1 2. The Arthur-Selberg trace formula for GL(2) 3 3.

Cusp forms and Hecke operators 7 Congruence subgroups of SL2(Z) 7 Weak modular forms 10 Cusps and Fourier expansions of modular forms 12 Hecke rings 20 The level NHecke ring 24 The elements T(n) 29 Hecke operators 34 The original trace formula for Hecke operators was given by Selberg in Many improvements were made in subsequent years, notably by Eichler and Hijikata.

This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formula for the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt › Books › Science & Math › Mathematics.

The Fourier transforms of weighted orbital integrals on semisimple groups of real rank one, Journal für die reine und angewandte Mathematik (), ; MathRev, Zbl, abstract; The trace formula for Hecke operators over rank one lattices, Journal of Functional Analysis 84 (), ; MathRev, Zbl, abstract; Back ~hoffmann/ Hecke operators and algebraicity results 43 Exercises 45 Chapter 6.

The Eichler-Selberg trace formula 47 Eisenstein series of half-integral weight 47 Holomorphic projection 49 The Eichler-Selberg trace formula 50 Exercises 53 Appendices A1. The Poisson summation formula 54 A2. The gamma function and the Mellin transform 55 Lectures on Modular Forms and Hecke Operators KennethA.

Ribet WilliamA. Stein Janu We derive the trace formula for Hecke operators acting in the completely G-decomposable subspace of, where G is a real reductive Lie group and Γ is a lattice of rank one in G. If Γ is We study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank over any algebraic number field.

In particular, we express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Modular Symbols and Hecke Operators. One way to find optimal lattices for these problems is to enumerate all finitely many, locally optimal lattices.

A semi-classical trace formula for Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, Julyis a collection of papers presented at the Selberg Symposium, held at the University of Oslo.

This symposium contains 30 lectures that cover the significant contribution of Atle Selberg in the field of :// Read "The non-semi-simple term in the trace formula for rank one lattices., Journal für die reine und angewandte Mathematik (Crelle's Journal)" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your :// Abstract.

In this paper, a zeta integral for the space of binary cubic forms is associated with the subregular unipotent contribution to the geometric side of the Arthur trace formula for the split exceptional group G :// 1). So, the previous setup for the collection of lattices K, Kranging over the open compact subgroups of G(A n), is contained in the current one.

A similar connection can be made for general G, where however a single subgroup Kwill correspond to a nite set of lattices in G(F 1) In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices E 7, E 8 and E 8 ⊕ A 1, with arbitrary Arthur’s theory, we deduce properties of the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and :// Don Zagier.

This webpage contains a list of my publications, and also links to the PDF files of all papers (but not of books; you'll have to either go to the bookstore or else pirate your own copies) the further formal manipulations allow one to prove a formula close to the one of Kottwitz.

The key new observations of [25], with precursors occuring in [24] and [23], are the following. The same method even works if one allows a nontrivial level K p at p, by reinterpreting the cohomology of the Shimura variety of level K pKp as the. Hecke operators into the picture (i.e., to consider the equidistribution of Hecke eigenvalues).

Thus, let now G be a reductive group deﬁned over a number ﬁeld F and S a ﬁnite set of places of F containing the set S ∞ of all archimedean :// Number Theory Books, P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.)N.

Koblitz, Graduate T Springer Algorithmic Number Theory, Vol. 1, E. Bach and J. Shallit, MIT Press, August ; Automorphic Forms and Representations, D.

Bump, CUP ; Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical Society Series of When n D2, Hijikata[7]used knowledge of N.0/=k 0 to compute the trace formula of Hecke operators. Analogously, when one derives a trace formula for Brandt matrices[10], one obtains as a byproduct a means to compute class numbers of certain orders in quaternion algebras, some of