We present an algorithm for computing the class number of the quadratic number field of discriminant d. The algorithm terminates unconditionally with the correct answer and, under the GRH, executes… (More)

We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a… (More)

The calculations had been planned some time in advance, but had in fact to be carried out in great haste. If it had not been for the fact that the computer remained in serviceable condition for an… (More)

We describe the construction of a database of genus 2 curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated L-function. This… (More)

We generalize the method of [Bo03] to prove a version of the converse theorem of JacquetLanglands with relaxed conditions on the twists by ramified idèle class characters.

We verify the Selberg eigenvalue conjecture for congruence groups of small squarefree conductor, improving on a result of Huxley [20]. The main tool is the Selberg trace formula which, unlike… (More)

I n March of this year, my student, Ce Bian, announced the computation of some “degree 3 transcendental L-functions” at a workshop at the American Institute of Mathematics (AIM). This article aims to… (More)

We consider the second of Mullin's sequences of prime numbers related to Euclid's proof that there are infinitely many primes. We show in particular that it omits infinitely many primes, confirming a… (More)

A Test for Identifying Fourier Coefficients of Automorphic Forms and Application to Kloosterman Sums Andrew R. Booker To cite this article: Andrew R. Booker (2000) A Test for Identifying Fourier… (More)