The boundary of the ordinary open string world sheet is the real line. Along with the usual
open string, one can consider p-adic open strings whose world sheet has as boundary the p …

Then we interchange bk_i andbk, and we leave the other b1 unchanged. The vectors b'_ 1
and b and the numbers Iukk_ 1'ILk_If, 11kj'Iik—1'Iik'for j< k—1 and for 1> k, have now to be …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

The third edition differs from the previous two in some fairly minor corrections and a number
of additions. Both of these are based on remarks and advice from readers of the earlier …

Bridging the gap between elementary number theory and the systematic study of advanced
topics, A Classical Introduction to Modern Number Theory is a well-developed and …

This book presents the essentials of harmonic analysis on locally compact groups in a
concise and accessible form. The text provides necessary background on Banach algebras …

The goal of this book is to present local class field theory from the cohomo logical point of
view, following the method inaugurated by Hochschild and developed by Artin-Tate. This …

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis
on certain connections with number theory. The ancient" congruent number problem" is the …

This book is an account of the combinatorics of projective spaces over a finite field, with
special emphasis on one and two dimensions. With its successor volumes, Finite projective …

Having built our foundation, we can now apply the general theory to the specific case of the
field ℚ of rational numbers. Extending our scope to include all fields of algebraic numbers …