Related papers: Lecture Notes on Quadratic Forms and their Arithme…

These notes are based on some lectures that the author gave at the University of Campinas - UNICAMP. The notes are in Portuguese, and deal with some methods of mathematics applied to Fluid Mechanics.

We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…

We obtain transformation formulas for quadratic character sums with quartic and cubic polynomial arguments.

This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required…

These notes introduce some of the basic mathematical and physical tools neccessary for theoretical investigations into the thermodynamics properties of light in cavities. The notes were created while preparing for a project in this area…

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.

Based on the works of M. Marshall on multirings, we propose the fundamentals for a \textbf{non reduced} abstract quadratic forms theory in general coefficients on rings, with the machinery of multirings and multifields.

We study cliques in graphs arising from quadratic forms where the vertices are the elements of the module of the quadratic form and two vertices are adjacent if their difference represents some fixed scalar. We determine structural…

An exposition of the basic geometry of twistor integrals, intended for mathematicians.

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…

These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.

The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.

This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…

This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.

We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.

These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.

In this paper, we are interested in the interplay between integral ternary quadratic forms and class numbers. This is partially motivated by a question of Petersson.

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…