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A Course in Arithmetic
TLDR
In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.Abstract:
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.read more
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Applied Conformal Field Theory
TL;DR: In this paper, an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory, is given, with a focus on conformal theories in d dimensions.
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The Algebraic and Geometric Theory of Quadratic Forms
TL;DR: The classical theory of symmetric bilinear forms and quadratic forms: Bilinear form Quadratic form forms over rational function fields Function fields of quadrics Bilinverse forms and algebraic extensions $u$-invariants Applications of the Milnor conjecture on the norm residue homomorphism of degree two Algebraic cycles: Homology and cohomology Chow groups Steenrod operations Category of Chow motives Quadratically forms and cyclic cycles as mentioned in this paper.
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Fermat’s Last Theorem
TL;DR: The authors of as mentioned in this paper give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this paper, and they are also grateful to A. Washington for their helpful comments.
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Lectures on K3 Surfaces
TL;DR: Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular and each chapter ends with questions and open problems.
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Chiral four-dimensional heterotic strings from self-dual lattices
TL;DR: In this paper, a lattice constructions of ten-dimensional heterotic strings can be applied to four dimensions, based on an extension of Narain's lattices by including the bosonized world-sheet fermions and ghosts, and uses conformal field theory as its starting point.