Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character

We evaluate the action of Hecke operators on Siegel Eisenstein series of arbitrary degree, level and character. For square-free level, we simultaneously diagonalise the space with respect to all the Hecke operators, computing the eigenvalues explicitly, and obtain a multiplicity-one result. For arbitrary level, we simultaneously diagonalise the space with respect to the Hecke operators attached to primes not dividing the level, again computing the eigenvalues explicitly.Comment: to appear, Internat. J. Number Theor

Top Quark Physics: Summary

This talk summarizes recent progress in top quark physics studies for high energy linear electron-positron colliders as presented at the LCWS2000 Workshop at Fermilab. New results were presented for top pair production at threshold and in the continuum, as well as for top production at $\gamma\gamma$ colliders.Comment: 7 pages, Latex, uses aipproc.sty; plenary talk presented at Linear Collider Workshop 2000, Fermilab, Batavia, IL, Oct. 24--28, 200

Gluon Radiation in Top Production and Decay at Lepton Colliders

In this talk we discuss gluon radiation in top production and decay. After reviewing results for hadron colliders we consider soft gluon radiation at lepton colliders and present gluon distributions that are potentially sensitive to production-decay interference effects.Comment: 8 pages including 4 figures, LaTeX; talk presented at the Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, Batavia, IL, Nov. 6--9, 199

Some relations on Fourier coefficients of degree 2 Siegel forms of arbitrary level

We extend some recent work of D. McCarthy, proving relations among some Fourier coefficients of a degree 2 Siegel modular form $F$ with arbitrary level and character, provided there are some primes $q$ so that $F$ is an eigenform for the Hecke operators $T(q)$ and $T_1(q^2)$

Action of Hecke operators on Siegel theta series II

Given a Siegel theta series and a prime p not dividing the level of the theta series, we apply to the theta series the n+1 Hecke operators that generate the local Hecke algebra at p. We show that the average theta series is an eigenform and we compute the eigenvalues

Hecke operators on Hilbert-Siegel modular forms

We define Hilbert-Siegel modular forms and Hecke "operators" acting on them. As with Hilbert modular forms, these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert-Siegel forms we identify several families of natural identifications between certain spaces of modular forms. We associate the Fourier coefficients of a form in our product space to even integral lattices, independent of a basis and choice of coefficient rings. We then determine the action of the Hecke operators on these Fourier coefficients, paralleling the result of Hafner and Walling for Siegel modular forms (where the number field is the field of rationals)