scispace - formally typeset
Open AccessBook

A Course in Arithmetic

Reads0
Chats0
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

Citations
More filters
Posted Content

Tensor field theory with applications to quantum computing

TL;DR: In this article, the success and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution.
Journal ArticleDOI

Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis.

TL;DR: In this paper, the spectral operator can be thought of intuitively intuitive given c 0, and a survey of earlier work can be found in Section 5.1.1].
Journal ArticleDOI

Conformal field theory and genus-zero function fields

TL;DR: One-loop partition functions of rational conformal field theories are finite linear combinations of modular invariants associated with projective modular functions of a modular subgroup as mentioned in this paper, and for normal subgroups with a genus-zero fundamental region, the functions which lead to physically acceptable partition functions are extremely limited in number, and can be found explicitly.
Book ChapterDOI

Rational Points on Twisted K3 Surfaces and Derived Equivalences

TL;DR: Using a construction of Hassett and Verilly-Alvarado, this article derived equivalent twisted K3 surfaces over Q, Q 2 and R, where one has a rational point and the other does not.
Book ChapterDOI

Replicable Functions: An Introduction

TL;DR: In this article, the authors survey the theory of replicable functions and its ramifications from number theory to physics, and present a survey of the connections between number theory and particle physics.