$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight

Mathematics – Number Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on $\Gamma_{0}(4N)$ for $N=1,2,4$. A proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications we obtain congruences of Borcherds exponents, congruences of quotient of Eisentein series and congruences of values of $L$-functions at a certain point are also studied. Furthermore, the congruences of the Fourier coefficients of Siegel modular forms on Maass Space are obtained using Ikeda lifting.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight 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 $p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral Weight will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-552317

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.