L-FUNCTIONS FOR HOLOMORPHIC FORMS ON GSp(4)×GL(2) AND THEIR SPECIAL VALUES
نویسنده
چکیده
We provide an explicit integral representation for L-functions of pairs (F, g) where F is a holomorphic genus 2 Siegel newform and g a holomorphic elliptic newform, both of squarefree levels and of equal weights. When F, g have level one, this was earlier known by the work of Furusawa. The extension is not straightforward. Our methods involve precise double-coset and volume computations as well as an explicit formula for the Bessel model for GSp(4) in the Steinberg case; the latter is possibly of independent interest. As an application, we prove an algebraicity result for a critical value of L(s, F × g). This is in the spirit of known results on critical values of triple product L-functions, also of degree 8, though there are significant differences.
منابع مشابه
Iwahori–spherical representations of GSp(4) and Siegel modular forms of degree 2 with square-free level
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