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Abstract Geometric Langlands predicts an isomorphism between Whittaker coefficients of Eisenstein series and functions on the moduli space of$$\check {N}$$-local systems. We prove this formula by interpreting Whittaker coefficients of Eisenstein series as factorization homology and then invoking Beilinson and Drinfeld’s formula for chiral homology of a chiral enveloping algebra.
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Fourier expansion of light‐cone Eisenstein series
Abstract In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic ‐space. As a consequence, we obtain results on location of all poles of these Eisenstein series as well as their supremum norms. We use this information to get new results on counting rational points on spheres.
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- Award ID(s):
- 1651563
- PAR ID:
- 10441995
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Journal of the London Mathematical Society
- Volume:
- 108
- Issue:
- 6
- ISSN:
- 0024-6107
- Format(s):
- Medium: X Size: p. 2175-2247
- Size(s):
- p. 2175-2247
- Sponsoring Org:
- National Science Foundation
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