Related papers: Elementare Zahlentheorie
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
This paper is an introduction to classical polylogarithms and is an expanded version of a talk given by the author at the Motives conference. Topics covered include, monodromy; the polylogarithm local systems; Bloch's constructions of…
This is an elementary exposition of the basic descent theorems for algebraic schemes over fields (Grothendieck, Weil, ...).
This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal…
Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
This is a textbook on Fourier Series, suitable for both undergraduate and graduate courses. The textbook is endowed with exercises, and full solutions are provided at the end of the book.
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
This is a draft version of Part I of a three-part textbook on quantum field theory.
This short note contains elementary evaluations of some Euler sums.
This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.
This small overview of the General Theory is the kind of summary I would have liked to have read, before embarking in a comprehensive study of the General Theory at the time I was a student. As shown here, the main ideas are quite simple…
This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding…