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A fast new algorithm is used compute the zeros of 10 6 quadratic character L-functions for negative fundamental discrim-inants with absolute value d > 10 12. These are compared to the 1-level density, including various lower order terms. These terms come from, on the one hand the Explicit Formula, and on the other the L-functions Ratios Conjecture. The… (More)

An algorithm is given to efficiently compute L-functions with large conductor in a restricted range of the critical strip. Examples are included for about 24000 dihedral Galois representations with conductor near 10 7. The data shows good agreement with a symplectic random matrix model.

- JEFFREY STOPPLE
- 2001

- JEFFREY STOPPLE
- 2010

The trace formula for SL{2,Z) can be developed for vector-valued functions which satisfy an automorphic condition involving a group representation n. This paper makes this version explicit for the class of representations which can be realized as representations of the finite group PSL(2,Z/q) for some prime q. The body of the paper is devoted to computing,… (More)

We apply Tatuzawa's version of Siegel's theorem to derive two lower bounds on the size of the principal genus of positive definite binary quadratic forms.

- Jeffrey Stopple
- 2006

- JEFFREY STOPPLE
- 2003

An algorithm is given to efficiently compute, for large discriminant, L-functions of characters on the class group of a complex quadratic field. This is an analog in conductor aspect of the Odlyzko-Schönhage algorithm to compute the Riemann zeta function. Examples are included for about 21000 L-functions with conductor near 10 7. The data shows good… (More)

- JEFFREY STOPPLE
- 2003

- JEFFREY STOPPLE
- 2003

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