The first negative Hecke eigenvalue of a Siegel cusp form of genus two
Let be a positive integer, a finite field of cardinality with . In this paper, inspired by [6, 3, 4] and using a slightly different method, we study the fluctuations in the number of -points on the curve given by the affine model , where is drawn at random uniformly from the set of all monic -th power-free polynomials of degree as . The method also enables us to study the fluctuations in the number of -points on the same family of curves arising from the set of monic irreducible...
For any prime number p > 3 we compute the formal completion of the Néron model of J0(p) in terms of the action of the Hecke algebra on the Z-module of all cusp forms (of weight 2 with respect to Γ0(p)) with integral Fourier development at infinity.
It is well known that every can be expanded to an infinite Lüroth series in the form of where for all . In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets are completely determined, where is an integer-valued function defined on , and as .