Henry T
- Research Program Mentor
PhD candidate at Brown University
Expertise
Elementary number theory, analytic number theory, algebraic number theory, root systems
Bio
Hi, I'm Henry! I have a BS in Mathematics from the University of Minnesota Twin Cities where I was advised by Adrian Diaconu. Currently, I am a PhD candidate at Brown University under the advisement of Jeff Hoffstein. My primary interests are in analytic number theory, in particular, Weyl group multiple Dirichlet series, automorphic forms, and subconvexity. Outisde of mathematics I enjoy staying active by dancing Lindy Hop, biking, calisthenics training, bouldering, and skiing. I have interests in artifical brains, existential AI risk, mycelium, whiskey, and perfumery. I am active in the rationalist community and am an avid fan of the NYT Spelling Bee.Project ideas
Fundamental Properties Dirichlet Series
The aim of this project is to explore one of the most fundamental tools in an analytic number theorist's toolbox: Dirichlet Series. The classical Dirichlet series is the infamous Riemann zeta function. Student's will understand what a Dirichlet series is, in addition to the following: - Arithmetic functions (Mobius, Euler Totient, Von Mangoldt, etc) - Dirichlet convolution - Euler products - The Selberg identity As an application, students will understand how properties of Dirichlet series encode facts about prime numbers (in particular the statement of the prime number theorem). The student should have a solid background in calculus and algebra. Coding expierence is not necessiary but would be helpful to compute lots of examples.