Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f (x)g(x) d (x)+ K ∑ k=1 Nk ∑ i=0 Mk,if (ak)g (ak), where the mass points ak belong to [−1, 1], and Mk,i > 0(i = 0, 1, . . . , Nk). In this paper, we obtain generalized trace formula and asymptotics of the averagedTuran determinant for the Sobolev-type orthogonal pol...

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.

The aim here is to continue the investigation in [1] of Jacobians of a Klein surface and also to correct an error in [1].

We give a method for finding rational equations of genus 2 curves whose jacobians are abelian varieties Af attached by Shimura to normalized newforms f ∈ S2(Γ0(N)). We present all the curves corresponding to principally polarized surfaces Af for N ≤ 500.

In this paper, we examine the characteristics of titles (average length, proportion of titles with subtitles, proportion of interrogatory, and indicative titles) and how they changed over a substantial period of time (half a century). We consistently analyze core literature in five diverse fields, in order to probe the usage of titles as a disciplinary identity building tool. In addition, we st...

We construct the Nahm transform for Higgs bundles over a Riemann surface of genus at least 2 as hyperholomorphic connections on the total space of the tangent bundle of its dual Jacobian. 2000 MSC: 53C07, 53C26

The total variation T V (u) of the Jacobian determinant of non-smooth vector fields u has recently been studied in [2]. We focus on the subclass u(x) = ϕ(x/|x|) of homogeneous extensions of smooth functions ϕ : ∂B n → R n. In the case n = 2, we explicitely compute T V (u) for some relevant examples exhibiting a gap with respect to the total variation |DetDu| of the distributional determinant. W...