Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.

background

https://www.math.bgu.ac.il/~szpruchd/The_Langlands-Shahidi_Method_for_the_metaplectic_group_and_applications.pdf

A Course in Arithmetic

The Langlands-Shahidi Method for the metaplectic group and applications Thesis submitted for the degree "Doctor of Philosophy"

We give simple proofs of the Davenport--Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the number of 3-torsion elements in the class groups of quadratic fields having bounded discriminant. We also establish second main terms for these theorems, thus proving a conjecture of Roberts. Our arguments provide natural interpretations for the various constants appearing in these theorems in terms of local masses of cubic rings.

On the Davenport-Heilbronn theorems and second order terms

The rising sea: Grothendieck on simplicity and generality

Cloud computing has emerged as the most dominant computational paradigm in recent times. There are tremendous benefits for enterprises adopting cloud technologies. It provides resources and services on demand, pay-as-you go basis. This includes infrastructure, platform and software services. But there are still a number of security threats and challenges associated with utilizing cloud computing. A proper access control is the fundamental security requirement in any cloud environment, to avoid unauthorized access to the cloud systems. As cloud computing supports multi-tenancy and has a various categories of users with different sets of security requirements, traditional access control models and policies cannot be used. This paper discusses on various access control models used for cloud environment and presents a detailed requirement analysis for developing an access control, specifically for the cloud. A comprehensive study on various security problems associated with outsourced data on the cloud and their existing solutions are also described, with the future research directions.

/pdf/a-comprehensive-survey-and-analysis-on-access-control-20dxzhbos9.pdf

A Comprehensive Survey and Analysis on Access Control Schemes in Cloud Environment

The theory of “zeta functions of fractal strings” has been initiated by the first author in the early 1990s and developed jointly with his collaborators during almost two decades of intensive research in numerous articles and several monographs. In 2009, the same author introduced a new class of zeta functions, called “distance zeta functions,” which since then has enabled us to extend the existing theory of zeta functions of fractal strings and sprays to arbitrary bounded (fractal) sets in Euclidean spaces of any dimension. A natural and closely related tool for the study of distance zeta functions is the class of “tube zeta functions,” defined using the tube function of a fractal set. These three classes of zeta functions, under the name of “fractal zeta functions,” exhibit deep connections with Minkowski contents and upper box dimensions, as well as, more generally, with the complex dimensions of fractal sets. Further extensions include zeta functions of relative fractal drums, the box dimension of which can assume negative values, including minus infinity. We also survey some results concerning the existence of the meromorphic extensions of the spectral zeta functions of fractal drums, based in an essential way on earlier results of the first author on the spectral (or eigenvalue) asymptotics of fractal drums. It follows from these results that the associated spectral zeta function has a (nontrivial) meromorphic extension, and we use some of our results about fractal zeta functions to show the new fact according to which the upper bound obtained for the corresponding abscissa of meromorphic convergence is optimal.

/pdf/fractal-zeta-functions-and-complex-dimensions-of-relative-1dh0dppmhg.pdf

A Course in Arithmetic

Citations

The Langlands-Shahidi Method for the metaplectic group and applications Thesis submitted for the degree "Doctor of Philosophy"

On the Davenport-Heilbronn theorems and second order terms

The rising sea: Grothendieck on simplicity and generality

A Comprehensive Survey and Analysis on Access Control Schemes in Cloud Environment

Fractal zeta functions and complex dimensions of relative fractal drums

Related Papers (5)

Sphere packings, lattices, and groups

The Arithmetic of Elliptic Curves

An Introduction to the Theory of Numbers

Introduction to analytic number theory

Number Theory