Description
The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne-Beilinson cohomology. The text includes many exercises to test comprehension and challenge readers of all abilities.
A friendly and concise introduction to the Mahler measure - a fascinating subject in contemporary mathematics.
About the Author
Francois Brunault is Associate Professor at Ecole Normale Superieure, Lyon in France, and is a member of the Mathematical Society of France. He is an arithmetic geometer with interest in elliptic curves, modular forms and L-functions, both from a theoretical and explicit point of view. Wadim Zudilin is Professor of Pure Mathematics at Radboud University Nijmegen, known for his results that make use of special functions in number theory, in particular, about the irrationality for the values of Riemann's zeta function at positive integers. He co-authored the book Neverending Fractions: An Introduction to Continued Fractions (Cambridge, 2014).
Reviews
'... the book will serve as a great introduction to the subject of Mahler's measure, in some of its manifold variations, with a special focus on its links with special values of L-functions. It is particularly suited for a student or research seminar, as well as for individual work, because of its concise nature, which emphasizes the most important points of the theory, while not leaving out crucial details when needed.' Riccardo Pengo, zbMATH
Book Information
ISBN 9781108794459
Author Francois Brunault
Format Paperback
Page Count 180
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 270g
Dimensions(mm) 227mm * 151mm * 10mm
A friendly and concise introduction to the Mahler measure - a fascinating subject in contemporary mathematics.
About the Author
Francois Brunault is Associate Professor at Ecole Normale Superieure, Lyon in France, and is a member of the Mathematical Society of France. He is an arithmetic geometer with interest in elliptic curves, modular forms and L-functions, both from a theoretical and explicit point of view. Wadim Zudilin is Professor of Pure Mathematics at Radboud University Nijmegen, known for his results that make use of special functions in number theory, in particular, about the irrationality for the values of Riemann's zeta function at positive integers. He co-authored the book Neverending Fractions: An Introduction to Continued Fractions (Cambridge, 2014).
Reviews
'... the book will serve as a great introduction to the subject of Mahler's measure, in some of its manifold variations, with a special focus on its links with special values of L-functions. It is particularly suited for a student or research seminar, as well as for individual work, because of its concise nature, which emphasizes the most important points of the theory, while not leaving out crucial details when needed.' Riccardo Pengo, zbMATH
Book Information
ISBN 9781108794459
Author Francois Brunault
Format Paperback
Page Count 180
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 270g
Dimensions(mm) 227mm * 151mm * 10mm
