L-functions for holomorphic forms on GSp(4) x GL(2) and their special values

Abhishek Saha

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)


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. We apply our integral representation to prove an algebraicity result for a critical special value of L(s, F \times 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.
Original languageEnglish
Pages (from-to)1773-1837
Number of pages65
JournalInternational Mathematics Research Notices
Issue number10
Early online date13 Feb 2009
Publication statusPublished - 2009

Bibliographical note

48 pages, typos corrected, some changes in Sections 6 and 7, other minor changes


  • math.NT
  • math.RT
  • 11F46; 11F67; 11F70; 22E50; 22E55;


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