Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

Invitation to the mathematics of Fermat-Wiles

Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles'' extraordinary proof. Furthermore, it places these concepts in their historical context.This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat''s last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle.Key Features* Rigorously presents the concepts required to understand Wiles'' proof, assuming only modest undergraduate level math * Sets the math in its historical context* Contains several themes that could be further developed by student research and numerous exercises and problems* Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat''s last theorem* Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat''s last theorem