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Boundedness of denominators of special values of the L-functions for modular forms

For a cuspidal Hecke eigenform $F$ for $Sp_n(Z)$ and a Dirichlet character $χ$ let $L(s,F,χ,St)$ be the standard $L$-function of $F$ twisted by $χ$. Boecherer showed the boundedness of denominators of the algebraic part of $L(m,F,χ,St)$ at a critical point $m$ when $χ$ varies. In this paper, we give a refined version of his result We also prove a similar result for the products of Hecke $L$ functions of primitive forms for $SL_2(Z)$.

preprint2022arXivOpen access
Hidenori Katsurada
math.NT
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Hidenori Katsurada

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