Rigid Irregular Connections And Wildly Ramified L Adic Local Systems Of Type G2
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Rigid Irregular Connections And Wildly Ramified L Adic Local Systems Of Type G2
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Author : Konstantin Jakob
language : en
Publisher:
Release Date : 2018
Rigid Irregular Connections And Wildly Ramified L Adic Local Systems Of Type G2 written by Konstantin Jakob and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Rigid Local Systems
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 1996
Rigid Local Systems written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform.
Introduction To Number Theory
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Author : Trygve Nagell
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Introduction To Number Theory written by Trygve Nagell 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 2021-07-21 with Education categories.
A special feature of Nagell's well-known text is the rather extensive treatment of Diophantine equations of second and higher degree. A large number of non-routine problems are given. Reviews & Endorsements This is a very readable introduction to number theory, with particular emphasis on diophantine equations, and requires only a school knowledge of mathematics. The exposition is admirably clear. More advanced or recent work is cited as background, where relevant … [T]here are welcome novelties: Gauss's own evaluation of Gauss's sums, which is still perhaps the most elegant, is reproduced apparently for the first time. There are 180 examples, many of considerable interest, some of these being little known. -- Mathematical Reviews
Nonstandard Analysis Axiomatically
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Author : Vladimir Kanovei
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Nonstandard Analysis Axiomatically written by Vladimir Kanovei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
On Multiply Monotone Functions And Their Laplace Transforms
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Author : Richard Edmund Williamson
language : en
Publisher:
Release Date : 1955
On Multiply Monotone Functions And Their Laplace Transforms written by Richard Edmund Williamson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with Laplace transformation categories.
The Distribution Of Prime Numbers
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Author : Albert Edward Ingham
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-28
The Distribution Of Prime Numbers written by Albert Edward Ingham 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 1990-09-28 with Mathematics categories.
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
Mathematical Theory Of Scattering Resonances
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Author : Semyon Dyatlov
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-10
Mathematical Theory Of Scattering Resonances written by Semyon Dyatlov 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 2019-09-10 with Frequencies of oscillating systems categories.
Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
The Legacy Of Kurt Sch Tte
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Author : Reinhard Kahle
language : en
Publisher: Springer Nature
Release Date : 2020-08-10
The Legacy Of Kurt Sch Tte written by Reinhard Kahle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-10 with Mathematics categories.
This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.
Mathematics Frontiers And Perspectives
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Mathematics Frontiers And Perspectives written by Vladimir Igorevich Arnolʹd 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 2000 with Mathematics categories.
A celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians.
Galois Groups Over
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Author : Y. Ihara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Galois Groups Over written by Y. Ihara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is the offspring of a week-long workshop on "Galois groups over Q and related topics," which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987. The organizing committee consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference focused on three principal themes: 1. Extensions of Q with finite simple Galois groups. 2. Galois actions on fundamental groups, nilpotent extensions of Q arising from Fermat curves, and the interplay between Gauss sums and cyclotomic units. 3. Representations of Gal(Q/Q) with values in GL(2)j deformations and connections with modular forms. Here is a summary of the conference program: • G. Anderson: "Gauss sums, circular units and the simplex" • G. Anderson and Y. Ihara: "Galois actions on 11"1 ( ••• ) and higher circular units" • D. Blasius: "Maass forms and Galois representations" • P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" • W. Feit: "Some Galois groups over number fields" • Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk • U. Jannsen: "Galois cohomology of i-adic representations" • B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" • B. Mazur: "Deforming GL(2) Galois representations" • K. Ribet: "Lowering the level of modular representations of Gal( Q/ Q)" • J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" • J.