Mathematical Research Letters

Volume 17 (2010)

Number 5

On the congruences primes of Saito-Kurokawa lifts of odd square-free level

Pages: 977 – 991

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n5.a14

Author

Jim Brown (Department of Mathematical Sciences, Clemson University, Clemson, SC 29631)

Abstract

In this paper we extend a conjecture of Katsurada’s characterizing the congruence primes of Saito-Kurokawa lifts of weight $\k$ and full level in terms of the divisibility of $L_{\alg}(\k,f)$ to the case of odd square-free level. After stating the conjecture, we provide evidence for the conjecture by constructing a congruence.

Full Text (PDF format)