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Table Of Integrals Series And Products

Tables of integrals

An overview 1. Graph theory 2. Number theory 3. PSL2(q) 4. The graphs Xp,q Appendix A. 4-regular graphs with large girth Index Bibliography.

Elementary Number Theory, Group Theory, and Ramanujan Graphs: An Overview

The aim of this paper is a better understanding for the eigenstates of the asymmetric quantum Rabi model by Lie algebra representations of . We define a second order element of the universal enveloping algebra of , which, through the action of a certain infinite dimensional representation of , provides a picture of the asymmetric quantum Rabi model equivalent to the one drawn by confluent Heun ordinary differential equations. Using this description, we prove the existence of level crossings in the spectral graph of the asymmetric quantum Rabi model when the symmetry-breaking parameter is equal to , and conjecture a formula that ensures likewise the presence of level crossings for general . This result on level crossings was demonstrated numerically by Li and Batchelor in 2015, investigating an earlier empirical observation by Braak (2011). The first analysis of the degenerate spectrum was given for the symmetric quantum Rabi model by Kuś in 1985. In our picture, we find a certain reciprocity (or -symmetry) for if the spectrum is described by representations of . We further discuss briefly the non-degenerate part of the exceptional spectrum from the viewpoint of infinite dimensional representations of having lowest weight vectors.

https://iopscience.iop.org/article/10.1088/1751-8121/aa649b/pdf

Symmetry of asymmetric quantum Rabi models

The present world of vehicle technology is inclined to develop Electric Vehicles (EVs) with various optimized features. These vehicles need frequent charging which takes a longer time to charge up. Therefore, scheduling of vehicles in charging stations is required. Besides, the information of the EVs and its location is also stored by the charging stations and therefore creates a concern of EV privacy. Various researches are going on to solve these problems; however, an efficient privacy-preserving solution is less practiced till date. In this paper, a framework for Electric Vehicle (EV) charging is discussed. The framework uses the concept of Matching Market to identify a charging station and uses the lattice-based cryptography for secure communications. The matching market considers multiple factors to provide the best allocation of charging station and cryptography ensures security and privacy preservation. The use of lattice-based cryptographic hash SWIFFT avoids heavy computation. This usage of matching market and lattice cryptography, more specifically signcryption for EV charging framework are the highlights of the solution and add-ons to the novel features. Overall, the presented framework is efficient in terms of computation and communication cost, satisfaction ratio, slot ratio, charging latency and load balancing index. The performance metrics are compared with recent developments in this field.

A Privacy-Preserving Secure Framework for Electric Vehicles in IoT Using Matching Market and Signcryption

We introduce the Hurwitz-type spectral zeta functions for the quantum Rabi models, and give their meromorphic continuation to the whole complex plane with only one simple pole at $s=1$
 . As an application, we give the Weyl law for the quantum Rabi models. As a byproduct, we also give a rationality of Rabi–Bernoulli polynomials introduced in this paper.

Spectral zeta functions for the quantum rabi models

We elaborate an explicit version of the relative trace formula on PGL(2) over a totally real number field for the toral periods of Hilbert cusp forms along the diagonal split torus. As an application, we prove (i) a spectral equidistribution result in the level aspect for Satake parameters of holomorphic Hilbert cusp forms weighted by central L-values, and (ii) a bound of quadratic base change L-functions for Hilbert cusp forms with a subconvex exponent in the weight aspect. Keyword: relative trace formulas, central L-values, subconvexity estimates.

Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms

Asymptotic behaviors of means of central values of automorphic L-functions for GL(2)

An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms

In this paper, we study regularized periods of cusp forms and Eisenstein series on $GL(2)$ introduced by Masao Tsuzuki.

/pdf/regularized-periods-of-automorphic-forms-on-gl-2-4kl6p9x8tw.pdf

Shingo Sugiyama

Papers

Spectral zeta functions for the quantum rabi models

Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms

Asymptotic behaviors of means of central values of automorphic L-functions for GL(2)

An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms

Regularized periods of automorphic forms on $gl(2)$