Mathematical Connections Seminar: Jason Rosenhouse

January 29, 2026 4:15–5:30 p.m.

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Melissa Marie Hernandez-Alvarez
mhernandezalvarez@hmc.edu
909.607.3618

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“Dirichlet’s Theorem and the Rise of Analytic Number Theory”

Abstract

In 1837, Peter Dirichlet proved the following theorem: If a and d are relatively prime integers, then the arithmetic progression a, a+d, a+2d, . . . contains infinitely many prime numbers. His proof ushered in a revolution in number theory because it relied in a critical way on complex analysis. The use of analytic methods to solve problems in number theory was a tremendous innovation at the time. We shall consider some of the details of Dirichlet's proof, focusing on understanding why there is a deep connection between these seemingly unrelated branches of mathematics. Throughout, we will be more concerned with the ideas underlying the proof than we will with presenting an excessive amount of technical detail.

This event is for: faculty, staff, students

Community Connections events provide opportunities for HMC faculty, students and staff to cultivate community, foster open conversations and share important information as together we live out our mission and shape the future of the College.