no code implementations • 26 Jan 2021 • Boris Dubrovin, Di Yang, Don Zagier
For each of the simple Lie algebras $\mathfrak{g}=A_l$, $D_l$ or $E_6$, we show that the all-genera one-point FJRW invariants of $\mathfrak{g}$-type, after multiplication by suitable products of Pochhammer symbols, are the coefficients of an algebraic generating function and hence are integral.
Algebraic Geometry Mathematical Physics Differential Geometry Mathematical Physics Exactly Solvable and Integrable Systems
no code implementations • 6 Jan 2021 • Elba Garcia-Failde, Don Zagier
We prove that a curious generating series identity implies Faber's intersection number conjecture (by showing that it implies a combinatorial identity already given in arXiv:1902. 02742) and give a new proof of Faber's conjecture by directly proving this identity.
Combinatorics Algebraic Geometry 05E14, 14H10, 14N10
no code implementations • 31 Dec 2020 • Danylo Radchenko, Don Zagier
In this paper we study two functions $F(x)$ and $J(x)$, originally found by Herglotz in 1923 and later rediscovered and used by one of the authors in connection with the Kronecker limit formula for real quadratic fields.
Number Theory
