Cuspidality of symmetric powers with applications

By Henry H. Kim, F. Shahidi. 2002

317 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/8c7d85d865642416122553569a2c6973d71b66a0

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. V. Blomer
2. P. Michel
3. Gergely Harcos
4. A. Raghuram
5. Akshay Venkatesh
6. R. Munshi
7. J. Cogdell
8. Jianya Liu

In Discrete Mathematics and Combinatorics

1. W. Gan
2. P. Michel
3. F. Shahidi
4. V. Blomer
5. J. Cogdell
6. Farrell Brumley
7. M. Asgari
8. Richard Harris

In Mathematical Physics

1. P. Michel
2. V. Blomer
3. W. Gan
4. Gergely Harcos
5. A. Raghuram
6. J. Cogdell
7. F. Shahidi
8. Akshay Venkatesh

Citations in the corpus

• Twisted L-Functions Over Number Fields and Hilbert’s Eleventh Problem (2009, unknown): “Currently θ =1 / 9i s known by the work of Kim and Shahidi [ KiS ], while the Ramanujan–Petersson conjecture predicts θ =0 . Theorem 1. For any e> 0 one has L(1/2 ,π ⊗ χ) � π,χ∞,K,e (N q)”
• On the complex moments of symmetric power $L$-functions at $s = 1$ (2004, methodology): “Hypothesis Sym(f) is known unconditionally for k up to 4: it is tautological if k = 1 and follows from the work of Gelbart/Jacquet for k = 2 and from the more recent works of Kim/Shahidi and Kim when k = 3, 4 [5, 15, 16, 14].”
• On the Ramanujan conjecture over number fields (2010, background): “Owing to the existence of proven cases of functoriality in low rank, there are certain small values of n for which Hn(δ) holds for a smaller δ; for example Kim-Shahidi [13] prove H2(1/9).”
• On the Special Values of Certain Rankin-Selberg L-Functions and Applications to Odd Symmetric Power L-Functions of Modular Forms (2008, background): “Acknowledgements: It is a pleasure to thank Don Blasius, Günter Harder, Michael Harris, Paul Garrett, Ameya Pitale and Freydoon Shahidi for their interest and helpful discussions.”
• The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II (2006, methodology): “Note that Hypothesis Hθ is known for θ = 7 64 thanks to the works of Kim, Shahidi and Sarnak [ KiSh ], [KiSa].”
• Subconvexity for Rankin-Selberg L-Functions of Maass Forms (2002, background): “by Kim and Shahidi [ KSh ], and most recently for θ =7 /64 by Kim and Sarnak [KS].”
• Generic transfer from GSp(4) to GL(4) (2004, background): “etric square L-function of Π is absolutely convergent for ℜ(s) >1 (cf. [12]) but this is only available presently for m≤ 4. When m= 2 we have the better bounds of H(1/9) for a general number field k[13] and H(7/64) for k= Q[12]. The Ramanujan conjecture demands H(0). Similarly, if π= ⊗′ vπv is a u”