arXiv subjects

Martin J. Dickson

Publications and source records attributed to Martin J. Dickson.

3 recordsLinked to original sources

arXiv2015

Hecke eigenvalues of Klingen--Eisenstein series of squarefree level

We compute the intertwining relation between the Hecke operators and the Siegel lowering operators on Siegel modular forms of arbitrary level $N$ and character $χ$ by using formulas for the action of the Hecke operators on Fourier expansions. Using an explicit description of the Satake compactification of $Γ_0^{(n)}(N) \backslash \mathfrak{H}_n$ when $N$ is squarefree we extend this to give intertwining relations for each cusp. As an application we give formulas for the action of Hecke operators on the space of Klingen--Eisenstein series of squarefree level $N$, for primes $p \nmid N$.

math.NT↗

arXiv2015

Fourier coefficients of degree 2 Siegel-Eisenstein series with trivial character at squarefree level

We compute the Fourier coefficients of all degree 2 Siegel-Eisenstein series of square-free level $N$ transforming with the trivial character. We then apply use these formulae to present some explicit examples of higher representation numbers attached to non-unimodular quadratic forms.

math.NT↗

arXiv2015

Local spectral equidistribution for degree 2 Siegel modular forms in level and weight aspects

We prove an equidistribution statement for the Satake parameters of the local representations attached to Siegel cusp forms of degree $2$ of increasing level and weight, counted with a certain arithmetic weight. We then apply this to compute the symmetry type of a similarly weighted distribution of the low-lying zeros of $L$-functions attached to these cusp forms.

math.NT↗