Welcome to EULER PRODUCT documentation!

sage-euler-product is a Python SageMath package implementing Eulerian Product for Number Theory

Documentation

Release:

Date:

Oct 14, 2025

AUTHORS:

• Olivier Ramaré : initial version CNRS, Institut de Mathématique de Marseille, Aix-Marseille Université

• Dominique Benielli Aix-Marseille Université, Laboratoire Informatique et des Systèmes Integration as SageMath package. Cellule de développement Institut Archimède

Contents:

• Tutorial Euler Product
  • Introduction and principles
  • Euler Product over every primes
  • Lattice Invariant Classes modulo \(q\)
  • Euler Product over primes in arithmetic progression
• Fast multi-precision computation of some Euler products
  • 1. Introduction
  • 2. Proof of Theorem 2 when \(F/H=1/(1-X)\)
  • 3. Proof of Theorem 2 in general
  • 4. Link with two other sets of inequalities
  • 5. Timing and implementation notes
• Installation EULER_PRODUCT
  • Euler Product for SageMath
• API Documentation
  • euler_product.lattice_invariant_euler_products
  • euler_product.utils_euler_product

Indices and tables

• Index

• Module Index

• Search Page