Half integral weight Hecke operators - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T11:31:44Z http://mathoverflow.net/feeds/question/109174 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109174/half-integral-weight-hecke-operators Half integral weight Hecke operators Eren Mehmet Kiral 2012-10-08T19:47:43Z 2012-10-08T20:13:25Z <p>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, $\kappa \in \frac 12 \mathbb{Z} - \mathbb{Z}$. I am searching for a formula which is similar to $$T_k(m)T_k(n) = \sum_{d|(m,n)} d^{k-1}T_k\left(\frac{mn}{d^2}\right)$$ in the case of full integral weight $k$. </p> <p>I suspect the answer to be exactly the same, since double coset decompositions in $\operatorname{GL}_2(\mathbb{R})^+$, and in its double cover should correspond to each other in a one-to-one fashion. The only difference being that the half integral Hecke operators are supported only on the squares.</p> <p>Am I missing anything?</p> http://mathoverflow.net/questions/109174/half-integral-weight-hecke-operators/109178#109178 Answer by GH for Half integral weight Hecke operators GH 2012-10-08T20:13:25Z 2012-10-08T20:13:25Z <p>I think you can find the answer <a href="http://front.math.ucdavis.edu/1208.4326" rel="nofollow">here</a>.</p>