The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms

Details The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms

2011-06-18

arxiv.org/abs/1106.3606v4

Mathematics

Number Theory

Preprint of an article accepted and pending publication in The International Journal of Number Theory, copyright 2011, World S

Scientific paper

10.1142/S179304211250042

From a result of Waldspurger, it is known that the normalized Fourier coefficients $a(m)$ of a half-integral weight holomorphic cusp eigenform $\f$ are, up to a finite set of factors, one of $\pm \sqrt{L(1/2, f, \chi_m)}$ when $m$ is square-free and $f$ is the integral weight cusp form related to $\f$ by the Shimura correspondence. In this paper we address a question posed by Kohnen: which square root is $a(m)$? In particular, if we look at the set of $a(m)$ with $m$ square-free, do these Fourier coefficients change sign infinitely often? By partially analytically continuing a related Dirichlet series, we are able to show that this is so.

Affiliated with

Also associated with

No associations

Rating

The Sign of Fourier Coefficients of Half-Integral Weight Cusp 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 The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-465369