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Showing 1 to 15 of 15 for “"trace formula"”.
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A relative trace formula approach to the stable trace formula on the unitary group
We develop a relative trace formula on GLₙ which can be compared to the stable trace formula on the unitary group. Locally, we prove the fundamental lemma and transfer. We also proof a character identity based on the transfer. Globally, we develop a (simple) relative trace formula and compared it …
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A Local Twisted Trace Formula and Twisted Orthogonality Relations
Around 1990, Arthur proved a local (ordinary) trace formula for real or p-adic connected reductive groups. The local trace formula is a powerful tool in the local harmonic analysis of reductive groups. One of the aims of this thesis is to establish a local twisted trace formula for certain …
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A Local Trace Formula and the Multiplicity One Theorem for the Ginzburg-Rallis Model
… conjecture, we are able to prove a local trace formula for the Ginzburg-Rallis model. Then by applying that trace formula, we prove a multiplicity formula for the Ginzburg-Rallis model for tempered representations. Using that multiplicity formula, we prove the multiplicity one theorem for …
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On Some Applications of a Generalized Dwork Trace Formula to L-functions associated to Exponential Sums over Galois Rings
Dwork’s trace formula is a seminal result proven by Bernard Dwork [Dwo60] (Section 2: Lemma 2), and it is one of the main ingredients in his celebrated proof of the rationality of the zeta function of an (affine or projective) algebraic variety over a finite field. In this thesis, we will prove a …
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Periodic orbit analysis of the Helmholtz equation in two-dimensional enclosures
… and the Mode Resonance Function Hypothesis.The trace formula, which is a sum over periodic orbits, approximates the level density for an acoustic enclosure. The trace formula in the concentric annulus domain is derived using a formulation for enclosures with continuous symmetry by Creagh and …
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Sato-Tate Problem for GL(3)
… of Goldfeld and Kontorovich on the Kuznetsov trace formula of Maass forms for SL(3,Z), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the p-th Hecke eigenvalue of Maass forms, with the rate of convergence. With a conjectured …
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Germ expansion, endoscopic transfer, and unitary periods
… For the second, we establish a new relative trace formula comparison conjectured by Jacquet that can be used to study unitary periods.
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Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions
… representation. In this thesis, using a relative trace formula approach, we prove the global twisted GGP conjecture in the unramified case, under some additional local assumptions on the quadratic extension and the automorphic representation. In particular, we reduce the required fundamental lemma …
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Explicit formulas for weighted orbital integrals for the inhomogeneous and semi-Lie arithmetic fundamental lemmas conjectured for the full spherical Hecke algebra
… fundamental lemma that appears in the relative trace formula approach to the Gan-Gross-Prasad conjectures, the arithmetic fundamental lemma was proposed by Wei Zhang and used in an approach to the arithmetic Gan-Gross-Prasad conjectures. The Jacquet-Rallis fundamental lemma was recently …
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Spectral Properties of Magnetic Edge States
… enables us to derive the semiclassical trace formula for magnetic billiards from first principles. We propose a spectral measure, which quantifies the intuitive notion of edge states. This density of edge states allows to analyse the interior and exterior spectra statistically, and to …
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Distribution of Holonomy about Closed Geodesics on Compact Hyperbolic 3-Manifolds
… theorems result from a non-spherical Selberg's trace formula which relates spectral information to lengths and holonomies of closed geodesics. Then, we show that although holonomy is equidistributed, there is typically a bias in the finer distribution. In particular, we show that a smoothed bias …
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The p-adic local langlands conjecture
… and in applications such as endoscopy and the trace formula, where an entire L-packet of representations contributes at once.
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Arithmetic transfers, modularity of arithmetic theta series and geometry of local-global Shimura varieties at parahoric levels
… particular their irreducible components. We also formulate and prove some local modularity questions. Secondly, we formulate some semi-Lie and group version arithmetic transfer conjectures at maximal parahoric levels, relating central derivatives of orbital integrals of explicit test functions to …
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Inverse methods for sound speed estimation in the ocean
… sound-speed based on the Deift-Trubowitz trace formula. Under certain assumptions, this algorithm can recover the sound speed profile in the seabed using pressure field measurements in the water column at low frequencies. The inversion algorithm requires solving a non-linear integral …
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Modified Stochastic Sine-Gordon Equation
The main focus of my dissertation is the Modified Stochastic Sine-Gordon Equation: utt = 2uxx − ut − sin(|u|^(&gamma)) + b(u, du/dt)dW/dt where &gamma > 0 is the parameter of the power of non-linearity, &delta &ge 0 is the magnitude of non-linearity, &alpha> 0 be the damping parameter, and &sigma …