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Results tagged with half-integral-weight
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user 16389
Questions about half-integral weight modular forms, and more generally automorphic representations associated to metaplectic groups.
6
votes
1
answer
483
views
Half integral weight Hecke operators
I would like to find a source giving the exact formula for the product of two Hecke operators $T_{\kappa}(n^2)$ and $T_\kappa(m^2)$ of half integral weight. That is, $\kappa \in \frac 12 \mathbb{Z} - …
1
vote
1
answer
324
views
Off critical line zeros for half integer weight $L$-functions
Let $f(z) = \sum_{n=1}^\infty A(n)n^{\frac{k-1}{2}}e(nz)$ be a modular form of weight $k$ for a half integer $k$. Put
$$L(s,f) = \sum_{n=1}^\infty \frac{A(n)}{n^s} $$
to be the $L$-function.
Further …
1
vote
0
answers
130
views
Sign of the functional equation of L function and Shimura lift
I would like to know what happens to the root number of a half integral weight automorphic form (holomorphic or not), i.e. the sign of the functional equation of its L-function when we apply the Shimu …