Abstract
We prove that there exist Salem numbers with trace –3 and every even degree . Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace –3 and degree , our result is optimal up to possibly the single value 32, for which it is expected there are no such numbers.
Acknowledgements
The authors would like to thank the referees for their valuable comments.