Seth Hardy
About
I am a final-year PhD student studying analytic and probabilistic number theory under the supervision of Professor Adam Harper. My research thus far has primarily focused on the study of random multiplicative functions.
I previously completed my MSci in Mathematics at University College London. During my 4th year, I completed a project titled 'Exploring recent developments in gaps between prime numbers' under the supervision of .
Research
鈥� Character sums over smooth numbers, with (2026). []
鈥� Helson's conjecture for smooth numbers, with (2025). []
鈥� The distribution of partial sums of random multiplicative functions with a large prime factor (2025). []
鈥� Bounds for exponential sums with random multiplicative coefficients (2024). International Mathematics Research Notices, rnae234. doi:. []
鈥� Almost sure bounds for a weighted Steinhaus random multiplicative function (2023). J. London Math. Soc., 110: e12979. doi:. [].
Talks
鈥� May 2026: Character sums over smooth numbers, Probability in Number Theory Seminar, CRM, Universit茅 de Montr茅al
鈥� March 2026: Character sums over smooth numbers, Heilbronn Number Theory , University of Bristol.
鈥� June 2025: Random multiplicative functions and their distribution, Oxford Random Matrix Theory .
鈥� March 2025: The distribution of random multiplicative functions with a large prime factor, Multiplicative Chaos in Number Theory Workshop, 神马福利影片.
鈥� March 2025: Random multiplicative functions and their distribution, , Institut Henri Poincar茅.
鈥� March 2025: Exponential sums with random multiplicative coefficients, de Th茅orie des Nombres de Nancy-Metz, Institut 脡lie Cartan de Lorraine.
鈥� January 2025: Exponential sums with random multiplicative coefficients, .
鈥� June 2024: Almost sure bounds for partial sums of a weighted Steinhaus random multiplicative function, London number theory study group.
鈥� May 2024: Exponential sums with random multiplicative coefficients, Bristol Linfoot Number Theory .
鈥� April 2024: Exponential sums with random multiplicative coefficients, London Junior Number Theory .
鈥� March 2024: Bounds for exponential sums with random multiplicative coefficients, Stanford Student Analytic Number Theory .
鈥� March 2024: Bounds for exponential sums with random multiplicative coefficients, FRG Grad .
Writing
Large values of Dirichlet polynomials - study group notes about a mean value of Heath-Brown. [pdf].
The Dickman function in probability (for MA946) [pdf].
My MSci Thesis: Gaps between prime numbers [pdf].
Teaching
Autumn Term 2025- Teaching Assistant for MA3B8 Complex Analysis.
Spring Term 2025 - Teaching Assistant for MA257 Introduction to Number Theory.
Autumn Term 2024- Teaching Assistant for MA4L6 Analytic Number Theory.
Spring Term 2024 - Supervisor for first year students.
Autumn Term 2023- Supervisor for first year students.
Spring Term 2023 - Teaching Assistant for MA257 Introduction to Number Theory.
Contact
