# Number Theory Seminar

Tuesday, January 21, 2020 — 1:30 PM EST

Anup Dixit, Queen's University

"On Ihara's conjecture and the localized Erdos-Kac theorem"

As a natural generalization of the Euler-Mascheroni constant $\gamma$, Ihara introduced the Euler-Kronecker constant $\gamma_K$ attached to a number field $K$. He conjectured that for cyclotomic fields $\mathbb{Q}(\zeta_n)$, this constant is always positive. In this talk, we will discuss a connection of this conjecture with the number of small prime factors of $p-1$, for primes $p$. Motivated by this, we also establish a localized Erdos-Kac type theorem in this context.

MC 5417

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