We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses.
|Number of pages||26|
|Early online date||10 Nov 2017|
|Publication status||Published - Dec 2018|
- Modular forms
- Converse theorems
- Ramanujan sums
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Dr M Lee
- School of Mathematics - Lecturer and Royal Society University Research Fellow
- Pure Mathematics
Person: Academic , Member