Abstract. In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues — completed (r + 1)-cycles. In particular, we give a geometric interpretation of these generalised Hurwitz numbers and derive a cut-and-join operator for completed (r+1)-cycles. We also prove a strong piecewise polynomiality property in ...

Price volatility is a major issue in liberalized electricity markets as far as risk management is concerned. In this paper we evaluate the impact of the Portuguese and Spanish electricity markets integration on the day-ahead market price volatility. For that purpose we develop an adaptive conjectural variations model which is implemented in GAMS language. We estimate the degree of competition i...

Let SQ(d) be the set of primes p for which there exists a number field K of degree ≤ d and an elliptic curve E/Q, such that the order of the torsion subgroup of E(K) is divisible by p. In this article we give bounds for the primes in the set SQ(d). In particular, we show that, if p ≥ 11, p 6= 13, 37, and p ∈ SQ(d), then p ≤ 2d + 1. Moreover, we determine SQ(d) for all d ≤ 42, and give a conject...

Let F be a totally real number field and let p be a finite prime of F , such that p splits completely in the finite abelian extension H of F . Stark has proposed a conjecture stating the existence of a p-unit in H with absolute values at the places above p specified in terms of the values at zero of the partial zeta-functions associated to H/F . Gross proposed a refinement of Stark’s conjecture...

We describe theorems and computational methods for verifying the Birch and Swinnerton-Dyer conjectural formula for specific elliptic curves over Q of analytic ranks 0 and 1. We apply our techniques to show that if E is a non-CM elliptic curve over Q of conductor ≤ 1000 and rank 0 or 1, then the Birch and Swinnerton-Dyer conjectural formula for the leading coefficient of the L-series is true for...

In this paper, we formulate conjectural formulas for the arithmetic intersection numbers of special cycles on unitary Shimura varieties with minuscule parahoric level structure. Also, prove that these conjectures are compatible all known results.