Frank Calegari

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math.NT2025

Arithmetic holonomy bounds and effective Diophantine approximation

Frank Calegari, Vesselin Dimitrov, Yunqing Tang

In this paper, we explore several threads arising from our recent joint work on arithmetic holonomy bounds, which were originally devised to prove new irrationality results based o…

math.NT2025

Modularity theorems for abelian surfaces

George Boxer, Frank Calegari, Toby Gee +1

We prove the modularity of a positive proportion of abelian surfaces over $Q$ . More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and ar…

math.NT2024

The linear independence of $1$ , $I^¶ (2)$ , and $L (2, I ¨ _{- 3})$

Frank Calegari, Vesselin Dimitrov, Yunqing Tang

We prove the irrationality of the classical Dirichlet L-value $L (2, I ¨ _{- 3})$ . The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier. I…

Arithmetic holonomy bounds and effective Diophantine approximation

Modularity theorems for abelian surfaces

The linear independence of 1, I^¶(2), and L(2,I¨−3​)

The linear independence of $1$ , $I^¶ (2)$ , and $L (2, I ¨ _{- 3})$