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1. |
Record Nr. |
UNINA9911109712103321 |
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Autore |
Tzanakis Nikos <1952-> |
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Titolo |
Elliptic diophantine equations / / by Nikos Tzanakis |
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Pubbl/distr/stampa |
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Berlin ; ; Boston : , : Walter de Gruyter, , [2013] |
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©2013 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (196 p.) |
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Collana |
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De Gruyter Series in Discrete Mathematics and Applications ; ; 2 |
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Disciplina |
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Soggetti |
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Diophantine equations |
Elliptic functions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front matter -- Preface -- Contents -- Chapter 1 Elliptic curves and equations -- Chapter 2 Heights -- Chapter 3 Weierstrass equations over C and R -- Chapter 4 The elliptic logarithm method -- Chapter 5 Linear form for the Weierstrass equation -- Chapter 6 Linear form for the quartic equation -- Chapter 7 Linear form for simultaneous Pell equations -- Chapter 8 Linear form for the general elliptic equation -- Chapter 9 Bound for the coefficients of the linear form -- Chapter 10 Reducing the bound obtained in Chapter 9 -- Chapter 11 S-integer solutions of Weierstrass equations -- List of symbols -- Bibliography -- Index |
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Sommario/riassunto |
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This book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit solution of elliptic Diophantine equations with the use of elliptic logarithms. The "art" of |
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solving this type of equation has now reached its full maturity. The author is one of the main persons that contributed to the development of this art. The monograph presents a well-balanced combination of a variety of theoretical tools (from Diophantine geometry, algebraic number theory, theory of linear forms in logarithms of various forms - real/complex and p-adic elliptic - and classical complex analysis), clever computational methods and techniques (LLL algorithm and de Weger's reduction technique, AGM algorithm, Zagier's technique for computing elliptic integrals), ready-to-use computer packages. A result is the solution in practice of a large general class of Diophantine equations. |
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2. |
Record Nr. |
UNINA9911150016203321 |
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Autore |
Kotkin Stephen |
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Titolo |
Steeltown, USSR : Soviet society in the Gorbachev era / / Stephen Kotkin |
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Pubbl/distr/stampa |
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Berkeley, : University of California Press, c1991 |
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ISBN |
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9786612356025 |
9781282356023 |
128235602X |
9780520911000 |
0520911008 |
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Descrizione fisica |
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1 online resource (364 p.) |
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Disciplina |
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Soggetti |
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Perestroĭka - Russia (Federation) - Magnitogorsk |
Magnitogorsk (Russia) Politics and government |
Soviet Union Politics and government 1985-1991 |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"A Centennial book." |
Includes index. |
First paperback printing with new epilogue 1992. |
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Nota di contenuto |
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Frontmatter -- Contents -- Preface To The Paperback Edition -- Preface -- Select Chronology -- 1. The Steel Cage: The Politics Of Economic Restructuring -- 2. Glasnost: A City Newspaper Rises, A |
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Theater Declines -- 3. Squaring The Circle: Reform Of And By The Communist Party -- 4. "Is Life Going To Go On Like This Forever?" Hopes Raised, Then Lowered -- 5. Socialism Is Dead! Long Live Socialism! Regeneration Through Elections? -- 6. A Stalin Mausoleum: The Past In The Present -- Afterword -- Epilogue -- Index |
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Sommario/riassunto |
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No one, not even Mikhail Gorbachev, anticipated what was in store when the Soviet Union embarked in the 1980s on a radical course of long-overdue structural reform. The consequences of that momentous decision, which set in motion a transformation eventually affecting the entire postwar world order, are here chronicled from inside a previously forbidden Soviet city, Magnitogorsk. Built under Stalin and championed by him as a showcase of socialism, the city remained closed to Western scrutiny until four years ago, when Stephen Kotkin became the first American to live there in nearly half a century.An uncommonly perceptive observer, a gifted writer, and a first-rate social scientist, Kotkin offers the reader an unsurpassed portrait of daily life in the Gorbachev era. From the formation of "informal" political groups to the start-up of fledgling businesses in the new cooperative sector, from the no-holds-barred investigative reporting of a former Communist party mouthpiece to a freewheeling multicandidate election campaign, the author conveys the texture of contemporary Soviet society in the throes of an upheaval not seen since the 1930s.Magnitogorsk, a planned "garden city" in the Ural Mountains, serves as Kotkin's laboratory for observing the revolutionary changes occurring in the Soviet Union today. Dominated by a self-perpetuating Communist party machine, choked by industrial pollution, and haunted by a suppressed past, this once-proud city now faces an uncertain future, as do the more than one thousand other industrial cities throughout the Soviet Union.Kotkin made his remarkable first visit in 1987 and returned in 1989. On both occasions, steelworkers and schoolteachers, bus drivers and housewives, intellectuals and former victims of oppression-all willingly stepped forward to voice long-suppressed grievances and aspirations. Their words animate this moving narrative, the first to examine the impact and contradictions of perestroika in a single community. Like no other Soviet city, Magnitogorsk provides a window onto the desperate struggle to overcome the heavy burden of Stalin's legacy. |
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