Beyond expansion, III: Reciprocal geodesics

Jean Bourgain, Alex Kontorovich

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We prove the existence of infinitely many low-lying and fundamental closed geodesics on the modular surface which are reciprocal, that is, invariant under time reversal. The method combines ideas from parts I and II of this series, namely, the dispersion method in bilinear forms, as applied to thin semigroups coming from restricted continued fractions.

Original languageEnglish (US)
Pages (from-to)3413-3435
Number of pages23
JournalDuke Mathematical Journal
Issue number18
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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