Download E-books Elliptic Diophantine Equations (de Gruyter Series in Discrete Mathematics and Applications) PDF

By Nikos Tzanakis

This e-book provides in a unified approach the attractive and deep arithmetic, either theoretical and computational, on which the specific answer of an elliptic Diophantine equation is predicated. It collects various effects and strategies which are scattered in literature. a few effects are even hidden at the back of a few workouts in software program programs, like Magma. This booklet is appropriate for college students in arithmetic, in addition to expert mathematicians.

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Download E-books Foliations II (Graduate Studies in Mathematics Series Volume 60) PDF

By Alberto Candel

This is often the second one of 2 volumes at the qualitative concept of foliations. For this quantity, the authors have chosen 3 specified issues: research on foliated areas, attribute periods of foliations, and foliated manifolds. each one of those is an instance of deep interplay among foliation conception and a few different highly-developed sector of arithmetic. In all instances, the authors current valuable, in-depth introductions, which result in extra examine utilizing the broad to be had literature. This finished quantity has anything to provide a vast spectrum of readers: from novices to complex scholars to specialist researchers. It includes workouts and plenty of illustrations. The ebook could make a sublime supplementary textual content for a issues path on the complex graduate point. ""Foliations I"" is quantity 23 within the AMS sequence, ""Graduate experiences in Mathematics"".

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Download E-books Singular Homology Theory from 1991, 1st edition (v. 127) PDF

The most function of this publication is to provide a scientific therapy of singular homology and cohomology conception. it truly is in a few feel a sequel to the author's prior publication during this Springer-Verlag sequence entitled Algebraic Topology: An creation. This past booklet is well now not a logical prerequisite for the current quantity. even though, it can definitely be effective for a potential reader to have an acquaintance with a few of the subject matters handled in that past quantity, equivalent to 2-dimensional manifolds and the funda­ psychological staff. Singular homology and cohomology thought has been the topic of a couple of textbooks within the final couple of a long time, so the fundamental define of the speculation in all fairness good proven. for that reason, from the viewpoint of the maths concerned, there might be little that's new or unique in a e-book comparable to this. nonetheless, there's nonetheless room for loads of sort and originality within the info of the exposition. during this quantity the writer has attempted to offer a simple therapy of the subject material, stripped of all pointless definitions, terminology, and technical equipment. He has additionally attempted, at any place possible, to stress the geometric motivation at the back of a number of the strategies.

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Download E-books A First Course in Modular Forms (Graduate Texts in Mathematics) PDF

By Fred Diamond

This booklet introduces the idea of modular types, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner idea; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian types linked to Hecke eigenforms. because it provides those principles, the ebook states the Modularity Theorem in a variety of varieties, touching on them to one another and concerning their functions to quantity conception. The authors think no history in algebraic quantity thought and algebraic geometry. routines are included.

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Download E-books Cubic Metaplectic Forms and Theta Functions PDF

By Nikolai Proskurin

The publication is an creation to the idea of cubic metaplectic varieties at the third-dimensional hyperbolic house and the author's examine on cubic metaplectic varieties on specified linear and symplectic teams of rank 2. the themes contain: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein sequence, cubic theta capabilities, Whittaker features. a unique procedure is constructed and utilized to discover Fourier coefficients of the Eisenstein sequence and cubic theta services. The e-book is meant for readers, with starting graduate-level heritage, attracted to extra examine within the thought of metaplectic kinds and in attainable purposes.

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Download E-books Higher Dimensional Birational Geometry (Advanced Studies in Pure Mathematics) PDF

This quantity comprises 4 papers written by way of contributors of the overseas convention on larger Dimensional Algebraic forms held on the learn Institute of Mathematical Sciences (RIMS) at Kyoto collage (Japan). instead of a standard court cases of the convention, the editors have compiled a variety of self reliant, complete expositions on issues of primary value in algebraic geometry: moduli areas of abelian surfaces, rational curves on algebraic types, third-dimensional flips, and the idea of elliptic fibrations. The authors - together with a Fields medalist and the founding father of primary leads to algebraic geometry - speak about the themes totally, giving entire proofs of recent effects, technical arrangements, and an old evaluation. The ebook is acceptable for graduate scholars and study mathematicians attracted to algebraic geometry.

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Download E-books Moduli of Double Epw-sextics (Memoirs of the American Mathematical Society) PDF

The writer reports the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $\bigwedge^3{\mathbb C}^6$ modulo the ordinary motion of $\mathrm{SL}_6$, name it $\mathfrak{M}$. it is a compactification of the moduli house of soft double EPW-sextics and consequently birational to the moduli house of HK $4$-folds of kind $K3^{[2]}$ polarized through a divisor of sq. $2$ for the Beauville-Bogomolov quadratic shape. the writer will ascertain the good issues. His paintings bears a powerful analogy with the paintings of Voisin, Laza and Looijenga on moduli and sessions of cubic $4$-folds.

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Download E-books Riemannsche Flächen (Springer-Lehrbuch) (German Edition) PDF

Die Theorie Riemannscher Flächen stellt der Autor als einen Mikrokosmos der Reinen Mathematik dar, in dem Methoden der Topologie und Geometrie, der komplexen und reellen research sowie der Algebra zusammenwirken. Viele Beispiele und Bilder, die in der historischen Entwicklung eine Rolle spielten, ergänzen die Darstellung. Die 2. Auflage wurde um eine genauere Betrachtung des Kleinschen 14-Ecks, ein Kapitel über die de Rhamsche Cohomologie und einen Abschnitt über die Lösung nicht-linearer Gleichungen der mathematischen Physik ergänzt.

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