Related papers: Beyond Endoscopy via Poisson Summation for GL(2,K)
The Landau-Selberg-Delange (LSD) method gives an asymptotic formula for the partial sums of a multiplicative function $f$ whose prime values are $\alpha$ on average. In the literature, the average is usually taken to be $\alpha$ with a very…
Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
In the paper "Extensional PERs" by P. Freyd, P. Mulry, G. Rosolini and D. Scott, a category $\mathcal{C}$ of "pointed complete extensional PERs" and computable maps is introduced to provide an instance of an \emph{algebraically compact…
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…
To define a minimal mathematical framework for isolating some of the characteristic properties of quantum entanglement, we introduce a generalization of the tensor product of graphs. Inspired by the notion of a density matrix, the…
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize…
We prove that for any k greater or equal to 2, given a smooth compact k-dimensional manifold and a multiplicative k-1-gerbe on a Lie group, together with an integrable connection, there is a line bundle on the corresponding…
In this paper an integral transform between spaces of nonstandard test functions on the affine space of dimension n is constructed. The integral transform satisfies a summation formula of Poisson type, which is derived from an analogue of…
In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument. We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler…
We present a new approach to far-from-equilibrium statistical mechanics, based on the concept of generalized entropy, which is a microscopically-defined generalization of Onsager-Machlup functional. In the case when a set of slow…
In arXiv:2212.14023 a decomposition of Gaussian measures on finite-dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…
We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group will not be…
Let $\mathbb{A}$ be the ring of adeles of a number field $k$ and $\pi$ be an irreducible cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A})$. In the previous work of the first author with Zhilin Luo, they introduced…
How to study a nice function on the real line? The physically motivated Fourier theory technique of harmonic analysis is to expand the function in the basis of exponentials and study the meaningful terms in the expansion. Now, suppose the…
Braverman and Kahzdan have introduced an influential conjecture on local functional equations for general Langlands $L$-functions. It is related to L. Lafforgue's equally influential conjectural construction of kernels for functorial…
Let $\Lambda$ be the von Mangoldt function and $r_{Q}\left(n\right)=\sum_{m_{1}+m_{2}^{2}+m_{3}^{2}=n}\Lambda\left(m_{1}\right)$ be the counting function for the numbers that can be written as sum of a prime and two squares (that we will…
In this paper we gives the Langlands parameters of Langlands' packets of discrete series using the twisted endoscopy as explained by Arthur; this holds for orthogonal, symplectic, unitary and G-Spin groups and gives the most simple proof…