Riemann Hypothesis and strongly Ramanujan complexes from GLn

Ming-Hsuan Kang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We investigate the Riemann Hypothesis on combinatorial zeta functions associated to finite quotients of the affine building of GLn. We prove that if the quotient complex is strongly Ramanujan then these zeta functions satisfy the Riemann Hypothesis. On the other hand, we show that the converse statement is also true provided the extra generic condition. In the end, we give an example to show that this generic condition is indeed necessary.

Original languageEnglish
Pages (from-to)281-297
Number of pages17
JournalJournal of Number Theory
Volume161
DOIs
StatePublished - 16 Dec 2014

Keywords

  • Building
  • GL
  • Ramanujan complexes
  • Riemann Hypothesis
  • Zeta functions

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