COMPUTING CENTRAL VALUES OF TWISTED L-SERIES, THE ...

-0.0282092 3571-0.0323612 3571COMPUTING CENTRAL VALUES OF TWISTED L-SERIES 210.045918Figure 8. The values R + q (10 8 )−R q for the elliptic curve 27A and2 ≤ q ≤ 3571 prime0.043458Figure 9. The values R − q (10 8 )−R q for the elliptic curve 27A and2 ≤ q ≤ 3571 primedistribution of the twisted L-series of the elliptic curves 27A and 15A by positiveand negative fundamental discriminants compared to the standard Gaussian.References[At-Le] Atkin, A. O. L. and Lehner, J.: Hecke operators on Γ 0 (m) Math. Ann. 185 (1970),134–160.[Bö-SP] Böcherer, S., Schulze-Pillot, R.: On a theorem of Waldspurger and on Eisenstein seriesof Klingen type. Math. Ann. 288 (1990), 361–388.[CNT] Computational Number Theory: http://www.ma.utexas.edu/cnt/.[CKRS] Conrey, J. and Keating, J. and Rubinstein, M. and Snaith, N.: On the frequency ofvanishing of quadratic twists of modular L-functions. Number theory for the millennium, I(Urbana, IL, 2000), 301–315.[CKRS2] Conrey, J. and Keating, J. and Rubinstein, M. and Snaith, N.: Random Matrix Theoryand the Fourier Coefficients of Half-Integral-Weight Forms. Exp. Math. 15 (2006), 67–82.[Cr] Cremona, J. Elliptic Curve Data. http://www.maths.nott.ac.uk/personal/jec/ftp/data/INDEX.html