# Manchester Number Theory Seminar - Vahagn Aslanyan

Dates: | 28 November 2023 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: Vahagn Aslanyan (Manchester)

Title: Multiplicative relations among differences of singular moduli

Abstract: I will report on recent joint work with Sebastian Eterovic and Guy Fowler where we study multiplicative relations among differences of singular moduli. A singular modulus is a value j(\tau) where j is the modular j-function and \tau is a quadratic irrational in the upper half-plane. Multiplicative relations between singular moduli were studied by Pila and Tsimerman; they showed that for every n there are only finitely many n-tuples of singular moduli which are multiplicative dependent. We generalise this to differences of singular moduli (which are of arithmetic interest) and show that outside certain special curves there are only finitely many (n+1)-tuples of singular moduli (x_1,…,x_n,y) such that x_1-y,…,x_n-y are multiplicatively dependent. I will explain how these special curves are constructed and why there are only finitely many of them.

Room: Frank Adams 1