Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms

Details Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms

2010-08-03

arxiv.org/abs/1008.0430v1

Mathematics

Number Theory

Scientific paper

We formulate and prove the analogue of the Ramanujan Conjectures for modular forms of half-integral weight subject to some ramification restriction in the setting of a polynomial ring over a finite field. This is applied to give an effective solution to the problem of representations of elements of the ring by ternary quadratic forms. Our proof develops the theory of half-integral weight forms and Siegel's theta functions in this context as well as the analogue of an explicit Waldspurger formula. As in the case over the rationals, the half-integral weight Ramanujan Conjecture is in this way converted into a question of estimating special values of members of a special family of L-functions. These polynomial functions have a growing number of roots (all on the unit circle thanks to Drinfeld and Deligne's work) which are shown to become equidistributed. This eventually leads to the key estimate for Fourier coefficients of half-integral weight cusp forms.

Affiliated with

Also associated with

No associations

Rating

Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-613549