The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometric-analytic aspects of function fields, but leaves an in-depth examination from this perspective to others.

Key topics and features:

* Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces

* Focuses on the Riemanna "Roch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more

* Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the Riemanna "Hurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules

* Explains both the similarities and fundamental differences between function fields and number fields

* Includes many exercises and examples to enhance understanding and motivate further study

The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 1-4 can serve as the base of an introductory undergraduate course for mathematicsmajors, while chapters 5-9 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Ragionamenti Di Cleandro, E Di Eudosso Sovra Le Lettere Al Provinciale: Recati Novellamente Nell'Italiana Favella Dall'Original Francese Gabriel Daniel, Eudoxus (Cnidius), Cleander Botagriffi, 1760

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Geschichte Von Frankreich, Volume 13 Gabriel Daniel

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Jusqu'a La Fin Du Regne De Louis Le Grand. Due to the very old age and scarcity of this book, many of the pages may be hard to read due to the blurring of the original text.

The 18th century was a wealth of knowledge, exploration and rapidly growing technology and expanding record-keeping made possible by advances in the printing press. In its determination to preserve the century of revolution, Gale initiated a revolution of its own: digitization of epic proportions to preserve these invaluable works in the largest archive of its kind. Now for the first time these high-quality digital copies of original 18th century manuscripts are available in print, making them highly accessible to libraries, undergraduate students, and independent scholars.Western literary study flows out of eighteenth-century works by Alexander Pope, Daniel Defoe, Henry Fielding, Frances Burney, Denis Diderot, Johann Gottfried Herder, Johann Wolfgang von Goethe, and others. Experience the birth of the modern novel, or compare the development of language using dictionaries and grammar discourses. ++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++British LibraryT122034A translation by William Darrell of 'Rponse aux Lettres provinciales de L. de Montalte, ou entretiens de Cleandre et d'Eudoxe' by Gabriel Daniel. (L. de Montalte is a pseudonym of Pascal). The imprint is false; printed at the English College press, Sa Cullen i.e. Saint-Omer]: Printed at Cullen i.e. St. Omer, by the English College Press], 1701. 4],431, 1]p.; 8