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Perron’s Formula and the Prime Number Theorem for Automorphic L-Functions
In this paper the classical Perron’s formula is modified so that it now depends no longer on sizes of individual terms but on a sum over a short interval. When applied to automorphic L-functions,…
A General Local Reconstruction Approach Based on a Truncated Hilbert Transform
This paper presents a general region-of-interest/volume- of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment.
Resonance between automorphic forms and exponential functions
AbstractLet f be a holomorphic cusp form of weight k for SL2(ℤ) and λf(n) its n-th Fourier coefficient. In this paper, the exponential sum ΣX < n ⩽ 2Xλf(n)e(αnB) twisted by Fourier coefficients λf(n)…
Subconvexity for Rankin-Selberg L-Functions of Maass Forms
Abstract.In this paper we prove a subconvexity bound for Rankin–Selberg L-functions $L(s,f \otimes g)$ associated with a Maass cusp form f and a fixed cusp form g in the aspect of the Laplace…
Distinguished representations and quadratic base change for $GL(3)$
Let E/F be a quadratic extension of number fields. Suppose that every real place of F splits in E and let H be the unitary group in 3 variables. Suppose that Π is an automorphic cuspidal…
Exact Interior Reconstruction from Truncated Limited-Angle Projection Data
Using filtered backprojection (FBP) and an analytic continuation approach, we prove that exact interior reconstruction is possible and unique from truncated limited-angle projection data, if we…
Interior Reconstruction Using the Truncated Hilbert Transform via Singular Value Decomposition.
The numerical results indicate that this approach runs two orders of magnitude faster than the iterative approach and produces an excellent region-of-interest (ROI) reconstruction that was previously impossible, demonstrating the feasibility of localized pre-clinical and clinical CT as a new direction for research on exact local image reconstruction.
Cone-beam pseudo-lambda tomography
In this paper, for the first time we define the concept of 3D pseudo-lambda tomography based on the 3D Calderon operator, and formulate an approximate local reconstruction algorithm for cone-beam…
Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions
Abstract We prove a weighted version of Selberg’s orthogonality conjecture for automorphic L-functions attached to irreducible cuspidal representations of GLm over ℚ. Using this weighted…