Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Graph
Search

Course

MATH-313: Number theory I.b - Analytic number theory

Summary

The aim of this course is to present the basic techniques of analytic number theory.

Lectures

Instructor

Petru Constantinescu

Official source

https://edu.epfl.ch/coursebook/en/number-theory-i-b-analytic-number-theory-MATH-313

Moodle Page

http://go.epfl.ch/MATH-313

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Summary

The aim of this course is to present the basic techniques of analytic number theory.

Lectures

Instructor

Petru Constantinescu

Official source

https://edu.epfl.ch/coursebook/en/number-theory-i-b-analytic-number-theory-MATH-313

Moodle Page

http://go.epfl.ch/MATH-313

About this result

Ontological neighbourhood

Mathematics

Number theory: Topics in number theory

Lectures in this course (15)

Arithmetic Functions: Multiplicative Functions and Dirichlet Convolution Log in to Mediaspace to watch this video

Covers multiplicative functions, Dirichlet convolution, and the Mobius function in arithmetic functions.

Summation Formulas of Arithmetic Functions Log in to Mediaspace to watch this video

Covers the Euler-Maclaurin summation formula and the method of convolution for evaluating arithmetic functions.

Functional Equation of Zeta and Hadamard Products Log in to Mediaspace to watch this video

Covers the functional equation of the Zeta function and the Hadamard factorization theorem.

Hadamard Factorization and Zeros of Zeta Log in to Mediaspace to watch this video

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

Classical Zero Free Region for Zeta and Explicit Formula I Log in to Mediaspace to watch this video

Establishes the classical zero free region for the Zeta function and starts the proof of the explicit formula for

\psi(x)

Related courses (30)

CS-101: Advanced information, computation, communication I

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics as diverse as mathematical reasoning, combinatorics, disc ...

MATH-101(en): Analysis I (English)

We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable. ...

MATH-101(g): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable. ...

MATH-502: Distribution and interpolation spaces

The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...

MATH-410: Riemann surfaces

This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...