Related papers: Character analysis using Fourier series

This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…

Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.

The q-characters of quantum loop algebras are very important objects in representation theory. In [20], we showed that q-characters factor as a power series of the form studied in [9] times a character, an important phenomenon which had…

We show that a short truncation of the Fourier expansion for a character sum gives a good approximation for the average value of that character sum over an interval. We give a few applications of this result. One is that for any $b$ there…

Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…

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

In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…

Various algebraic properties of Heilbronn's exponential sum can be deduced through the use of supercharacter theory, a novel extension of classical character theory due to Diaconis-Isaacs and Andre. This perspective yields a variety of…

In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…

For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…

One of the main features of eigenvalue matrix models is that the averages of characters are again characters, what can be considered as a far-going generalization of the Fourier transform property of Gaussian exponential. This is true for…

This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…

We estimate multiplicative character sums taken on the values of a non-homogeneous Beatty sequence $\{[\alpha n + \beta] : n =1,2,... \}$, where $\alpha,\beta\in\R$, and $\alpha$ is irrational. Our bounds are nontrivial over the same short…

Even today in Twenty First Century Handwritten communication has its own stand and most of the times, in daily life it is globally using as means of communication and recording the information like to be shared with others. Challenges in…

In this paper I present a new and unified method of proving character formulas for discrete series representations of connected Lie groups by applying a Chern character-type construction to the matrix factorizations of [FT] and [FHT3]. In…

The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…

We obtain nontrivial bounds for character sums with multiplicative and additive characters over finite fields over elements with restricted coordinate expansion. In particular, we obtain a nontrivial estimate for such a sum over a finite…

We propose a new task for assessing machines' skills of understanding fictional characters in narrative stories. The task, TVShowGuess, builds on the scripts of TV series and takes the form of guessing the anonymous main characters based on…

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…

Data is essential to performing time series analysis utilizing machine learning approaches, whether for classic models or today's large language models. A good time-series dataset is advantageous for the model's accuracy, robustness, and…