On the Ramanujan conjecture over number fields

By V. Blomer, Farrell Brumley. 2010

154 citations recorded by the source corpus.

We extend to an arbitrary number field the best known bounds towards the Ramanujan conjecture for the groups GL(n), n=2, 3, 4. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/020c2e477051c5426b1cda39b9f87ced34fbd2dd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Kannan Soundararajan
2. Peter Sarnak
3. Jesse Thorner
4. V. Blomer
5. M. Young
6. Gergely Harcos
7. Adam J Harper
8. Paul D. Nelson

In Discrete Mathematics and Combinatorics

1. Peter Sarnak
2. Kannan Soundararajan
3. Jesse Thorner
4. M. Young
5. Nicolas Templier
6. Paul D. Nelson

In Mathematical Physics

1. Kannan Soundararajan
2. Peter Sarnak
3. Jesse Thorner
4. V. Blomer
5. Gergely Harcos
6. M. Young
7. Paul D. Nelson
8. P. Michel

Citations in the corpus

• Weak subconvexity without a Ramanujan hypothesis (2018, result): “[4] V. Blomer and F. Brumley.”
• Notes on Thin Matrix Groups (2012, methodology): “Thanks to the referee for pointing me to the relevant applications in [Gromov and Guth 2012].”