1549380232-Automorphic_Forms_and_Applications__Sarnak_

[A] [AC] [As] [Bl] [Bl] [BDHI] [BG] [BH] [Car] [Cal] [Ca2 ] [Csh] [CS] [Cl] Bibliography J. Arthur, Endoscopic L - functions and ...

328 [Co] [CPSl] [CPS2] [CPS3] [CPSSJ [CKPSSl] [CKPSS2] [DI] [GJ] [GSl] [GS2] [HCJ [HT] [Hel] [He2] [JPSSl] [JPSS2] [KSh] [Kl] [K ...

[K3] [K4] [KS a] [KSl] [KS2] [KS3] [Ku] [Lal] [La2] [La3] [LRS] [Mi] [MWl] [MW2] [Mu] [Ra] [Sat] [Shl] [Sh2] [Sh3] [Sh4] [Sh5] B ...

330 [Sh6] [Sh7] [Sh8] [Sh9] [ShlO] [Shll] [SJ [Se] [Si] [Sp] [T] [W] [Z] FREYDOON SHAHID!, LANGLANDS-SHAHID! METHOD ___ Function ...

Arithmetical Quantum Chaos Audrey Terr as ...

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IAS/Park City Mathematics Series Volume 12, 2002 Arithmetical Quantum Chaos Audrey Terr as Abstract Physicists have long studied ...

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Introduction Lecture 1. Finite models This is a story of a tree related to the spectral theory of operators on Hilbert sp aces ...

336 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS Figure 1. The Tree of Quantum Chaos is t he Sinai billiard which is a square with ...

LECTURE 1. FINITE MODELS b d -+ - -- -----< - -----< -----< E - K -----< -----< ---- ---< -----< - - _« i ...

338 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS [,j acting on the finite dimensional Hilbert space rcm1 ~ L^2 (Mj) and we study th ...

LECTURE 1. FINITE MODELS 339 Exercise 2. Repeat the experiment that produced Figure 1 using uniformly distrib- uted matrices rat ...

340 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS the GOE distribution." Here GOE stands for Gaussian Orthogonal Ensemble -the eigen ...

LECTURE 1. FINITE MODELS 341 {Jn I((~+ iJn) = 0, Jn> 0} · For the normalized level spacings, replace Jn by Jn = 2 ~ Jnlo9Jn&g ...

342 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS p(s) = E"(s). Then p(s) ?". 0 and f 0 00 p(s)ds = 1. The Gaudin-Mehta distribution ...

LECTURE 1. FINITE MODELS 343 One says that r is arithmetic if there is a faithful rational representation (see Borel [14], p. 6) ...

344 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS spectrum of the non-tessellating [non-arithmetic] triangle, whose classical proper ...

LECTURE 1. F INITE MODELS 345 Basic Questions about Spectra of Finite Connected k-Regular Graphs Can non-isomorphic graphs ha ...

346 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS Margulis as well as Lubotzky, Phillips and Sarnak [53] construct examples of infin ...