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

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.

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Published 1 January 2010