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Analytic Number Theory
  • Language: en
  • Pages: 378

Analytic Number Theory

This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (?elementary?) and complex variable (?analytic?) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/

The Theory of Algebraic Numbers: Second Edition
  • Language: en
  • Pages: 175

The Theory of Algebraic Numbers: Second Edition

This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.

Elliptic Partial Differential Operators and Symplectic Algebra
  • Language: en
  • Pages: 130

Elliptic Partial Differential Operators and Symplectic Algebra

This investigation introduces a new description and classification for the set of all self-adjoint operators (not just those defined by differential boundary conditions) which are generated by a linear elliptic partial differential expression $A(\mathbf{x}, D)=\sum_{0\, \leq\, \left s\right \, \leq\,2m}a_{s} (\mathbf{x})D DEGREES{s}\;\text{for all}\;\mathbf{x}\in\Omega$ in a region $\Omega$, with compact closure $\overline{\Omega}$ and $C DEGREES{\infty }$-smooth boundary $\partial\Omega$, in Euclidean space $\mathbb{E} DEGREES{r}$ $(r\geq2).$ The order $2m\geq2$ and the spatial dimensio

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness
  • Language: en
  • Pages: 187

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness

This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)

Self-Similarity and Multiwavelets in Higher Dimensions
  • Language: en
  • Pages: 98

Self-Similarity and Multiwavelets in Higher Dimensions

Let $A$ be a dilation matrix, an$n \times n$ expansive matrix that maps a full-rank lattice $\Gamma \subset \R DEGREESn$ into itself. Let $\Lambda$ be a finite subset of$\Gamma$, and for $k \in \Lambda$ let $c_k$ be $r \times r$ complex ma

$v_1$-Periodic Homotopy Groups of $SO(n)$
  • Language: en
  • Pages: 106

$v_1$-Periodic Homotopy Groups of $SO(n)$

Computes the 2-primary $v_1$-periodic homotopy groups of the special orthogonal groups $SO(n)$; the method is to calculate the Bendersky-Thompson spectral sequence, a $K_*$-based unstable homotopy spectral sequence, of $\operatorname{Spin}(n)$.

Maximum Principles on Riemannian Manifolds and Applications
  • Language: en
  • Pages: 118

Maximum Principles on Riemannian Manifolds and Applications

Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.

The Space of Mathematics
  • Language: en
  • Pages: 440

The Space of Mathematics

None

Generative Complexity in Algebra
  • Language: en
  • Pages: 176

Generative Complexity in Algebra

Considers the behavior of $\mathrm{G}_\mathcal{C}(k)$ when $\mathcal{C}$ is a locally finite equational class (variety) of algebras and $k$ is finite. This title looks at ways that algebraic properties of $\mathcal{C}$ lead to upper or lower bounds on generative complexity.

Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
  • Language: en
  • Pages: 146

Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation

Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].