Sökning: "Riemann integral"

Visar resultat 1 - 5 av 11 uppsatser innehållade orden Riemann integral.

1. 1. The Riemann Hypothesis and the Distribution of Primes

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

   Författare :David Appelgren; Leo Tikkanen; [2023]
   Nyckelord :Riemann; Riemann Hypothesis; Zeta Function; Prime Number Theorem;

   Sammanfattning : The aim of this thesis is to examine the connection between the Riemannhypothesis and the distribution of prime numbers. We first derive theanalytic continuation of the zeta function and prove some of its propertiesusing a functional equation. LÄS MER

3. 2. Differentialekvationer med minne : Integration och konvergens

   Kandidat-uppsats, Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

   Författare :Josefine Ramstedt; [2023]
   Nyckelord :Differentialekvationer med minne; Riemann-Stieltjes integral; konvergens; integration;

   Sammanfattning : Differentialekvationer med minne är ett redskap som ofta används inom modellering i olika områden. Vid lösning av differentialekvationer använder man sig ofta av integrering, mer specifikt kan man använda sig av Riemann-Stieltjes integral. LÄS MER

4. 3. The Riemann Zeta Function and Prime Numbers

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

   Författare :Oskar Rune; Linus Envall; [2023]
   Nyckelord :;

   Sammanfattning : This thesis is the result of a literature study regarding the relationship between the Riemann zeta function and prime numbers. We introduce the $\zeta$ function, discussing its properties. Then, starting from Riemann's original series, we derive the Euler product formula and functional equation for $\zeta$. LÄS MER

5. 4. Complex Multiplicative Calculus and Mixed Problems

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

   Författare :Axel Lokrantz; [2022]
   Nyckelord :multiplicative integrals; multiplicative calculus; product integrals; geometric mean; continuous geometric mean; geometric mean of non-negative random variables; inequality of arithmetic and geometric means; A_G-G_A inequality; generalized Hölder s inequality; multiplicative vector spaces; multiplicative function spaces; exponential transition functor; logarithmic Riemann surface; lift; function lift; projection; function projection; lift-projection method; multivalued complex multiplicative integrals; geometric expectation; mixed differential equation; Lambert W function; W; M; w and m functions; Mathematics and Statistics;

   Sammanfattning : In this thesis we consider multiplicative integrals and derivatives on functions on the positive numbers, the logarithmic Riemann surface and the punctured complex numbers. Additive structures on the real and complex numbers are related to their multiplicative counterparts on the positive numbers and the logarithmic Riemann surface by defining exponential transition functors. LÄS MER

7. 5. The Henstock–Kurzweil Integral

   Kandidat-uppsats, Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

   Författare :Manolis David; [2020]
   Nyckelord :Henstock–Kurzweil integral; generalized Riemann integral; gauge integral; Denjoy–Perron integral; narrow Denjoy integral; Perron integral; non-absolute integration; Lebesgue outer measure; absolute integrability; fundamental theorem of calculus; convergence theorems; single variable calculus;

   Sammanfattning : Since the introduction of the Riemann integral in the middle of the nineteenth century, integration theory has been subject to significant breakthroughs on a relatively frequent basis. We have now reached a point where integration theory has been thoroughly researched to a point where one has to delve quite deep into a particular subject in order to encounter open conjectures. LÄS MER