Read Online Automorphic Forms and Poincare Series for Infinitely Generated Fuchsian Groups (Classic Reprint) - Lipman Bers | ePub
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The real analytic poincare series are a generalization of holomorphic poincare series, which yield, generically, functions of exponential growth (as opposed to the eisenstein series which have moderate growth) but which are still useful in the construction of automorphic forms.
Automorphic objects of weight 2 2k, so-called locally harmonic maass forms, which are locally har-monic, but have singularities along certain geodesics. Via some natural differential operators we can relate the lift to the shimura correspondence. For some kind of poincare series, this lift was considered by bringmann, kane and viazovska.
All modular forms of weight 2 can be expressed by eisenstein series. Joint with poincare series corresponding to products of harmonic siegel-maass forms.
Bell [3] poincaré series representations of automorphic forms, thesis, brown university, 1966. Bers [4] automorphic forms and poincaré series for infinitely.
Summer school, banff international research station (canada) the stable trace formula, automorphic forms, and galois representations. Three lectures on relations between automorphic representations and galois representations.
Apr 10, 2018 non-spherical poincaré series, cusp forms and l-functions for gl(3) - jack buttcane a short course on modular forms by prof.
Each chapter of the book concludes with a list of relevant computer programs from gl(n)pack, a mathematica add-on package developed by kevin broughan.
In: drinfeld modules, modular schemes and applications (alden-biesen, 1996), world.
We compute their fourier expansions, which yield zagier-type dualities and also yield a lift to skew-holomorphic jacobi-poincare series. Finally, we link har-monic maass-jacobi forms to different kinds of automorphic forms via a commutative diagram.
We explain how to compute the representation numbers in the coe cient formulas for q k;m; and the eisenstein series of bruinier and kuss p-adically to get an e cient algorithm. The main application is in constructing automorphic products.
Zuckerman in the case of weakly holomorphic modular forms of negative a generic harmonic maass form f to that linear combination of maass-poincaré series.
Our construction of modular forms will lead us to the poincaré series, and with the help of the petersson inner.
Aug 15, 2015 -automorphic function f: \mathbf h \rightarrow \bf c of suitable decay, we can form a relative poincaré series p_\gamma_\infty \backslash.
2 niebur-poincaré series and almost holomorphic modular forms.
Cuspidal automorphic forms constructed via poincare series, their non–vanishing and applications.
This depends on the existence of an appropriate system of poincaré series.
Automorphic form kleinian group discrete series discrete series representation poincare series these keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sl(2,z) automorphic forms and functions arise in closed string theory in at least two when r(z) can be represented as a convergent poincaré series.
Mar 2, 2009 form has meaning; it can touch us at such a primal level that our mind the stealth fighter and the cadillac show-car both have a menacing.
Automorphic forms and poincare series for infinitely generated fuchsian groups [bers, lipman] on amazon. Automorphic forms and poincare series for infinitely generated fuchsian groups.
Algebraic analytic apply attached automorphic forms automorphic representation bounded called character classical coefficients compact completely conjecture connected consider continuation converse theorem correspondence cusp forms cuspidal representation deduce defined definition denote eisenstein series entire equal estimate example exists.
Modern analysis of automorphic forms by example [ current version ] is my (485- page, for all r, the spectral decomposition of the associated poincare series.
Apr 6, 2015 alex kontorovich, rutgers experimental mathematics seminar, april 2, 2015 see part 2 at vimeo.
A modular form is a holomorphic function on the complex upper half plane satisfying poincaré series for these half-integral weight modular forms shows that.
It was followed by two volumes on elliptic modular functions by klein and fricke and two more volumes on automorphic functions also by klein and fricke. These four classic books are vast generalizations of the first volume and contain the highly original works of poincaré and klein on automorphic forms.
The goal of the present paper is to adjust methods of compactly supported poincaré series as developed in in order to show existence of various types of cuspidal automorphic forms with non-zero.
Poincaré series form a convenient tool to construct harmonic lifts. See theo- holomorphic, antiholomorphic and harmonic modular forms, with at most expo-.
Miraculously that these kinds of questions can be answered using modular/automorphic forms and furthermore automorphic forms can be understood by the langlands dual group. Example 1 (eisenstein series) for we define the weight eisenstein series it is easy to show that this series converges absolutely and converges uniformly in any compact.
The topics treated include the construction of fundamental domains, the notion of automorphic form on g\g and its relationship with the classical automorphic forms on x, poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, eisenstein.
The objective of the study is to investigate the behaviour of the inner products of vector-valued poincare series, for large weight, associated to submanifolds of a quotient of the complex unit ball and how vector-valued automorphic forms could be constructed via poincare series. In addition, it provides a proof of that vector-valued poincare series on an irreducible bounded symmetric domain.
A lot of resources i looked at, including wikipedia, thinks of automorphic forms as some sort of generalized periodic functions with respect to the action of discrete groups satisfying some extra.
Moreover, there are infinitely many linear relations among poincaré series.
(1987) poincare series, kloosterman sums, trace formulas, and automorphic forms for gl(n).
Asymptotics in automorphic spectral identities apr 16, 2010 2:45 364 vinh paul garrett distinguishing cuspforms from eisenstein series (cont'd) apr 09, 2010 2:45 364 vinh paul garrett distinguishing cuspforms from eisenstein series apr 02, 2010 2:45 364 vinh paul garrett fundamental solutions on sl(2n,c), cont'd mar 26, 2010 2:45 364 vinh.
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. We construct infinitely many modular forms and non-holomorphic automorphic.
Modular forms as well as zeros of eisenstein series for different groups.
Ratic forms, kloosterman and salié sums, are also of significance to both subjects. Origin-ally, they were discovered by poincaré as part of the fourier coefficients of the poincaré series, yet another set of important automorphic forms, but only gained (at)traction after they appeared in kloosterman’s refinement of the circle method.
Weak maass forms poincare series formed from i-bessel functions automorphic greens functions these have many applications for sl(2).
We construct generalized eisenstein series and poincare series, and prove that they are mixed automorphic forms.
The complete list of irreducible admissible representations of $\mathrmgl(2, \mathbbr)$ are known - principal series, discrete series, limit of discrete series, and finite dimensional representation-theory automorphic-forms.
Automorphic forms marcus berg karlstad university, sweden lise meitner symposium gothenburg, sep 2012 automorphic form: nonholomorphic eisenstein series.
ˆ for sk, the collection of cusp forms coming from galois representations.
The book by iwaniec provides the graduate student and the researcher wishing to acquire the basics on automorphic forms with a beautifully written and self-contained treatment of the classical modular and automorphic forms, kloosterman sums, hecke operators, automorphic l-functions, cusp forms and eisenstein series, spherical functions, theta.
We prove a formula for the petersson inner product of these poincaré series with any cuspidal automorphic form on \(sl_2(\mathbbr)^\sim\) of the same weight. From this formula and its proof, we derive a series of results on cusp forms of half-integral weight.
Sep 22, 2014 basically, if 2 shapes can be sqeezed or stretched to form another shape then they are homeomorphic.
Poincaré and eisenstein series for jacobi forms of lattice index. On the relation between jacobi forms and elliptic modular forms: talk given at the pure maths.
Captivated by stuart and revett's measured drawings and engravings, europe suddenly demanded greek forms.
Adic modular forms, eisenstein series, borcherds products, automorphic periods, oscillations of fourier coefficients of cusp forms poincare series kloosterman.
Apr 25, 2020 if the group γ acts fixed-point free, then automorphic forms define differential forms on the these series are called poincaré theta-series.
The seminar takes place on tuesdays, usually from 15:00 to 16:00 (german time, cest) via zoom. The meetings start 15 minutes before the talk with a short coffee break.
• string perturbation theory with d-branes and o-planes • some physics • modular forms, automorphic forms • review of a few old results (nonholomorphic eisenstein series).
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