Real zeros of holomorphic Hecke cusp forms
By Amit Ghosh, Peter Sarnak. 2011
56 citations recorded by the source corpus.
This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are sym- metric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity. Mathematics Subject Classification (2010). Primary: 11F11, 11F30. Sec- ondary: 34F05.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c37d5b1e19485ba5c180aa502aec416aad8fe363
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In Algebra and Number Theory
- A. Reznikov
- Amit Ghosh
- Peter Sarnak
- V. Blomer
- Gergely Harcos
- P. Michel
- Kannan Soundararajan
- Nicolas Templier
In Mathematical Physics
- A. Reznikov
- Amit Ghosh
- Peter Sarnak
- V. Blomer
- Gergely Harcos
- P. Michel
- Akshay Venkatesh
- Nicolas Templier
Citations in the corpus
- Nodal Domains of Maass Forms I (2012, methodology): “by Lemma 3.1, while the infinite range gives a term with exponential decay. We next provide a good approximation to F(x+iy) for a sequence of large values of y (this being the analog of Theorem 3.1 in [GS12], where a similar result was shown for holomorphic 14 Amit Ghosh, Andre Reznikov and Peter Sar”
- Multiplicative functions in short intervals (2015, unknown): “As observed by Ghosh and Sarnak in [10], the number of sign changes of λf (n) for n ≤ k1/2 (with k the weight of f) is related to the number of zeros of f on the vertical geodesic high in the cusp.”