A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums

Booker, Andrew R.

Experiment. Math., Tome 9 (2000) no. 3, p. 571-581 / Harvested from Project Euclid

Résumé

We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums $\pm S(1,1;p)\big/\hskip-1pt\sqrt p$ are not the coefficients of a Maass form with small level and eigenvalue. Source code and the calculated Kloosterman sums are available electronically.

Publié le : 2000-10-14
Classification: 11F30, 11L05, 11Y35

@article{1045759522,
     author = {Booker, Andrew R.},
     title = {A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums},
     journal = {Experiment. Math.},
     volume = {9},
     number = {3},
     year = {2000},
     pages = { 571-581},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1045759522}
}

Booker, Andrew R. A test for identifying Fourier coefficients of automorphic forms and application to Kloosterman sums. Experiment. Math., Tome 9 (2000) no. 3, pp.  571-581. http://gdmltest.u-ga.fr/item/1045759522/