Download or read book On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions written by Peter D. T. A. Elliott and published by American Mathematical Soc.. This book was released on 1994 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.
Download or read book On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions written by Peter D. T. A. Elliott and published by . This book was released on 1994 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Duality in Analytic Number Theory written by Peter D. T. A. Elliott and published by Cambridge University Press. This book was released on 1997-02-13 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with analytic number theory; many new results.
Download or read book Number Theory in Progress written by Kálmán Györy and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 1212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.
Download or read book Analytic Number Theory Modular Forms and q Hypergeometric Series written by George E. Andrews and published by Springer. This book was released on 2018-02-01 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Download or read book An Arithmetic Riemann Roch Theorem for Singular Arithmetic Surfaces written by Wayne Aitken and published by American Mathematical Soc.. This book was released on 1996 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following gives a development of Arakelov theory general enough to handle not only regular arithmetic surfaces but also a large class of arithmetic surfaces whose generic fiber has singularities. This development culminates in an arithmetic Riemann-Roch theorem for such arithmetic surfaces. The first part of the memoir gives a treatment of Deligne's functorial intersection theory, and the second develops a class of intersection functions for singular curves which behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves.
Download or read book The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux written by Christian Krattenthaler and published by American Mathematical Soc.. This book was released on 1995 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.
Download or read book Subgroup Lattices and Symmetric Functions written by Lynne M. Butler and published by American Mathematical Soc.. This book was released on 1994 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.
Download or read book Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions written by Stéphane Jaffard and published by American Mathematical Soc.. This book was released on 1996 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate several topics related to the local behavior of functions: pointwise Hölder regularity, local scaling invariance and very oscillatory "chirp-like" behaviors. Our main tool is to relate these notions to two-microlocal conditions which are defined either on the Littlewood-Paley decomposition or on the wavelet transform. We give characterizations and the main properties of these two-microlocal spaces and we give several applications, such as bounds on the dimension of the set of Hölder singularities of a function, Sobolev regularity of trace functions, and chirp expansions of specific functions.
Download or read book Degree 16 Standard L function of GSp 2 times GSp 2 written by Dihua Jiang and published by American Mathematical Soc.. This book was released on 1996 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic L-functions, introduced by Robert Langlands in the 1960s, are natural extensions of such classical L-functions as the Riemann zeta function, Hecke L-functions, etc. They form an important part of the Langlands Program, which seeks to establish connections among number theory, representation theory, and geometry. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic groups, and the relevant residue representations.
Download or read book Hilbert Modules over Operator Algebras written by Paul S. Muhly and published by American Mathematical Soc.. This book was released on 1995 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses the three-dimensional generalization of category, offering a full definition of tricategory; a proof of the coherence theorem for tricategories; and a modern source of material on Gray's tensor product of 2-categories. Of interest to research mathematicians; theoretical physicists, algebraic topologists; 3-D computer scientists; and theoretical computer scientists. Society members, $19.00. No index. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Manifolds with Group Actions and Elliptic Operators written by Vladimir I︠A︡kovlevich Lin and published by American Mathematical Soc.. This book was released on 1994 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies equivariant linear second order elliptic operators [italic capital]P on a connected noncompact manifold [italic capital]X with a given action of a group [italic capital]G. The action is assumed to be cocompact, meaning that [italic capitals]GV = [italic capital]X for some compact subset of [italic capital]V of [italic capital]X. The aim is to study the structure of the convex cone of all positive solutions of [italic capital]P[italic]u = 0.
Download or read book Automorphisms of the Lattice of Recursively Enumerable Sets written by Peter Cholak and published by American Mathematical Soc.. This book was released on 1995 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.
Download or read book Hilbert s Projective Metric and Iterated Nonlinear Maps written by Roger D. Nussbaum and published by American Mathematical Soc.. This book was released on 1988 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weyl Groups and Birational Transformations among Minimal Models written by Kenji Matsuki and published by American Mathematical Soc.. This book was released on 1995 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide a unified way of looking at the apparently sporadic Weyl groups connected with the classical geometry of surfaces, namely those with 1) the rational double points, 2) the Picard groups of Del Pezzo surfaces, 3) the Kodaira-type degenerations of elliptic curves, and 4) the Picard-Lefschetz reflections of [italic]K3-surfaces, by putting them together into the picture of 3-dimensional birational geometry in the realm of the recently established Minimal Model Theory for 3-folds.
Download or read book Algebraic and Analytic Geometry of Fans written by Carlos Andradas and published by American Mathematical Soc.. This book was released on 1995 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.
Download or read book Stable Networks and Product Graphs written by Tomás Feder and published by American Mathematical Soc.. This book was released on 1995 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structural and algorithmic study of stability in nonexpansive networks is based on a representation of the possible assignments of Boolean values for a network as vertices in a Boolean hypercube under the associated Hamming metric. This global view takes advantage of the median properties of the hypercube, and extends to metric networks, where individual values are now chosen from the finite metric spaces and combined by means of an additive product operation. The relationship between products of metric spaces and products of graphs then establishes a connection between isometric representation in graphs and nonexpansiveness in metric networks.
