This paper presents a Poincaré lemma for the Kostant comple x, used to compute geometric quantisation, when the polarisat ion is given by a Lagrangian foliation defined by an integrable system wit h non-degenerate singularities.

Let A be a modular elliptic curve over a totally real field F, and let E/F be a totally imaginary quadratic extension. In the event of exceptional zero phenomenon, we prove a formula for the derivative of the multivariable ...

Let N = 1 be a integer such that the modular curve X* 0 (N) has genus = 2. We prove that X* 0 (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X* 0 (N) is bielliptic over the base field for all ...

Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga–Sato variety over a suitable Shimura curve ...

El Teorema de Freiman és possiblement un dels teoremes més important de combinatòria aritmètica inversa: dona l'estructura d'un conjunt d'enters A sota la condició de que el cardinal del conjunt suma A+A sigui petit en ...

Heegner points play an outstanding role in the study of the Birch and Swinnerton-Dyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil L-series. ...

In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to ...

This article can be read as a companion and sequel to the authors’ earlier article on Stark points and p-adic iterated integrals attached to modular forms of weight one, which proposes a conjectural expression for the ...

The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional ...

Let XD be the Shimura curve associated with an indefinite rational quaternion algebra of reduced discriminant D>1. For each prime l|D, there is a natural cyclic Galois covering of Shimura curves XD,l → XD constructed by ...