Gorō Shimura Books

Geared towards readers with a foundational understanding of modular forms, this advanced text delves deeper into the subject, offering fresh insights that engage those seeking more than elementary treatment. It meticulously presents every definition and essential fact about classical modular forms in one variable, ensuring clarity while exploring complex concepts. This approach caters to the intellectual curiosity of advanced learners and enriches their understanding of the topic.

This book is divided into two parts: the first covers algebraic number theory and semisimple algebras, while the second focuses on classifying quadratic forms and quadratic Diophantine equations. It discusses methods for classification over algebraic number fields and integers, highlighting a new approach using Clifford algebras.

The book explores Dirichlet series and modular forms through both traditional and unconventional approaches. It is designed to be accessible for readers without prior knowledge of these subjects, making complex concepts easier to understand.

Reciprocity laws are pivotal in number theory, explored through roots of unity and complex multiplication of elliptic functions. Goro Shimura's work presents significant generalizations, detailing these laws via abelian varieties, theta functions, and modular functions, including Siegel modular functions. The book also delves into the zeta function of abelian varieties and the emerging field of algebraic relations among periods of abelian integrals. This comprehensive treatment covers topics previously unexplored, making it a vital resource for researchers in the field.

The life of Goro Shimura, a renowned mathematician, unfolds alongside a vivid portrayal of the mathematical community and its eccentricities. The narrative delves into Japan's experiences during WWII, offering insights into Shimura's perspectives on global events and human nature. Through his journey, readers gain a unique understanding of the intersection between mathematics and the broader socio-political landscape of his time.

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field." 103 of Shimura ́s most important papers are collected in four volumes. Volume II contains his mathematical papers from 1967 to 1977 and some notes to the articles.

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field." 103 of Shimura ́s most important papers are collected in four volumes. Volume III contains his mathematical papers from 1978 to 1988 and some notes to the articles.

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field.." 103 of Shimura ́s most important papers are collected in four volumes. Volume I contains his mathematical papers from 1954 to 1966 and some notes to the articles.

The collection features 103 significant papers by Goro Shimura, showcasing his influential contributions to arithmetical geometry and automorphic forms. Volume I includes his work from 1954 to 1966, along with notes that provide context to his articles. Recognized with the Steele Prize for Lifetime Achievement, Shimura's concepts have become foundational in number theory, with many notations bearing his name, reflecting his lasting impact on the field and inspiring further developments.

Goro Shimura's significant contributions to arithmetical geometry and automorphic forms are showcased in this collection of his essential papers. Volume II specifically features his influential work from 1967 to 1977, highlighting concepts that have become foundational in number theory. Accompanied by notes, this volume reflects the depth and impact of Shimura's research, which has inspired numerous developments in the field.