Sökning: "Dirichlet Series"

Visar resultat 1 - 5 av 7 uppsatser innehållade orden Dirichlet Series.

  1. 1. Regularizing An Ill-Posed Problem with Tikhonov’s Regularization

    Kandidat-uppsats, Linköpings universitet/Analys och didaktik; Linköpings universitet/Tekniska fakulteten

    Författare :Herman Singh; [2022]
    Nyckelord :Inverse problem; Ill-posed problems; Tikhonov’s regularization; Fourier series; Helmholtz equation;

    Sammanfattning : This thesis presents how Tikhonov’s regularization can be used to solve an inverse problem of Helmholtz equation inside of a rectangle. The rectangle will be met with both Neumann and Dirichlet boundary conditions. A linear operator containing a Fourier series will be derived from the Helmholtz equation. LÄS MER

  2. 2. Can We Predict Business Cycles With Natural Language Processing?

    D-uppsats, Handelshögskolan i Stockholm/Institutionen för nationalekonomi

    Författare :Albert Flak; [2020]
    Nyckelord :Business Cycles; Economic Narratives; Natural Language Processing NLP ; Latent Dirichlet Allocation LDA ; Word Embeddings;

    Sammanfattning : For centuries, many economists have attempted to solve the puzzle of business cycles; what explains them, and is it possible to predict them? The great amount of electronically available textual data, together with the recent advancements in unsupervised natural language processing are bound to offer new ways of analysing these perennial questions. Inspired with the emergence of narrative economics as a new field of economic analysis, I propose a novel research design to computationally extract business cycle sentiment from textual data on economic expectations. LÄS MER

  3. 3. The Dirichlet Series To The Riemann Hypothesis

    Kandidat-uppsats, Högskolan i Gävle/Avdelningen för elektronik, matematik och naturvetenskap

    Författare :Daud Nawaz; [2018]
    Nyckelord :;

    Sammanfattning : This paper examines the Riemann zeta-function and its relation to the prime distribution. In this work, I present the journey from the Dirichlet series to the Riemann hypothesis. Furthermore, I discuss the prime counting function, the Riemann prime counting function and the Riemann explicit function for distribution of primes. LÄS MER

  4. 4. An Introduction to Dirichlet Series

    Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Eda Dagasan; [2018]
    Nyckelord :Mathematics; Dirichlet Series; Riemann Zeta Function; Complex Analysis; Bohr s Theorem; Mathematics and Statistics;

    Sammanfattning : We establish the central convergence properties of ordinary Dirichlet series, including the classical result by Bohr, providing uniform convergence of the series where it has a bounded analytic continuation. We also derive a lower bound for the supremum of Dirichlet polynomials using Kronecker's theorem, of which we see one proof. LÄS MER

  5. 5. On the Asymptotic Behaviour of Sums of Two Squares : Theoretical and Numerical Studies of the Counting Function B(x)

    Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

    Författare :Ivar Eriksson; Lukas Gustafsson; [2018]
    Nyckelord :;

    Sammanfattning : Studying the distributions of special numbers is a fundamental area of research in number theory. This paper studies the distribution of sums of two squares using analytic number theory. The asymptotic behaviour of the corresponding counting function, B(x), is the object of study. LÄS MER