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On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions


On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions
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On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions


On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions
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Author : Peter D. T. A. Elliott
language : en
Publisher:
Release Date : 1994

On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions written by Peter D. T. A. Elliott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Arithmetic functions categories.




On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions


On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions
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AUDIOBOOK

Author : Peter D. T. A. Elliott
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions written by Peter D. T. A. Elliott and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.


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.



Analytic Number Theory Modular Forms And Q Hypergeometric Series


Analytic Number Theory Modular Forms And Q Hypergeometric Series
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Author : George E. Andrews
language : en
Publisher: Springer
Release Date : 2018-02-01

Analytic Number Theory Modular Forms And Q Hypergeometric Series written by George E. Andrews and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Mathematics categories.


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.



Duality In Analytic Number Theory


Duality In Analytic Number Theory
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Author : Peter D. T. A. Elliott
language : en
Publisher: Cambridge University Press
Release Date : 1997-02-13

Duality In Analytic Number Theory written by Peter D. T. A. Elliott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-13 with Mathematics categories.


Deals with analytic number theory; many new results.



Number Theory In Progress


Number Theory In Progress
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Author : Kálmán Györy
language : en
Publisher: Walter de Gruyter
Release Date : 2012-02-13

Number Theory In Progress written by Kálmán Györy and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-13 with Mathematics categories.


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.



An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces


An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces
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Author : Wayne Aitken
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

An Arithmetic Riemann Roch Theorem For Singular Arithmetic Surfaces written by Wayne Aitken and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.


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.



The Major Counting Of Nonintersecting Lattice Paths And Generating Functions For Tableaux


The Major Counting Of Nonintersecting Lattice Paths And Generating Functions For Tableaux
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Author : Christian Krattenthaler
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

The Major Counting Of Nonintersecting Lattice Paths And Generating Functions For Tableaux written by Christian Krattenthaler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.


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.



Subgroup Lattices And Symmetric Functions


Subgroup Lattices And Symmetric Functions
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Author : Lynne M. Butler
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Subgroup Lattices And Symmetric Functions written by Lynne M. Butler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.


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.



Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions


Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions
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Author : Stéphane Jaffard
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions written by Stéphane Jaffard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.


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.



Degree 16 Standard L Function Of Gsp 2 Times Gsp 2


Degree 16 Standard L Function Of Gsp 2 Times Gsp 2
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Author : Dihua Jiang
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Degree 16 Standard L Function Of Gsp 2 Times Gsp 2 written by Dihua Jiang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.


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.