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This work covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. It establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of weighted lattice point numbers, in particular the non-uniform distribution of lattice points. The book presents multi-dimensional techniques for periodization, describes weighted lattice point and ball numbers in georelevant "potato-like" regions, and discusses radial and angular non-uniform lattice point distribution.

Starting with the most basic notions, this text introduces all the key elements needed to read and understand current research in the field. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, clones, and free algebras. The second part covers topics that demonstrate the power and breadth of the subject, such as Jónsson¿s lemma, finitely and nonfinitely based algebras, primal and quasiprimal algebras, Murski¿¿s theorem, and directly representable varieties. Examples and exercises are included throughout the text.

First developed in the early 1980s by Lenstra, Lenstra, and Lov sz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.

This work covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. It establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of weighted lattice point numbers, in particular the non-uniform distribution of lattice points. The book presents multi-dimensional techniques for periodization, describes weighted lattice point and ball numbers in georelevant "potato-like" regions, and discusses radial and angular non-uniform lattice point distribution.

Finite geometry is an important, wide-ranging research area in mathematics with strong connections to algebra and combinatorics. This book introduces parallelisms and spreads. It covers topics such as partial spreads, spreadsets, quasifields, collineations, automorphisms and autotopisms.