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We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncom-pact finite volume Riemann surface S under deformation of the surface. Our calculations indicate that if the Teichmüller space of S is not trivial, then each cusp form has a set of deformations under which either the cusp… (More)

Let T p,k (x) be the characteristic polynomial of the Hecke operator Tp acting on the space of level 1 cusp forms S k (1). We show that T p,k (x) is irreducible and has full Galois group over Q for k ≤ 2000 and p < 2000, p prime.

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