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Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values
| Content Provider | Semantic Scholar |
|---|---|
| Author | Rendina, Angelo |
| Copyright Year | 2019 |
| Abstract | In this thesis, we study the arithmeticity of critical values of degree-8 tensor product L-functions attached to Siegel modular forms of genus 1 and 2. We show that the congruence between the Hecke eigenvalues of two cuspidal Siegel Hecke eigenforms of genus 2 implies a similar congruence between certain suitably normalised critical values of the associated degree-8 L-functions. This phenomenon is predicted by the Bloch-Kato conjecture, for which we therefore provide further evidence in this particular setting. We prove this by employing integral representation formulae, due to Saha, and B¨ocherer and Heim, linking critical L-values to iterated Pe- tersson inner products against diagonally restricted non-holomorphic Eisenstein series. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://etheses.whiterose.ac.uk/25473/2/angelorendna_phdthesis.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
