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Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2016, Volume 144, Issue 12, pp. 5061 - 5069
Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic... 
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 2016, Volume 144, Issue 12, pp. 5061 - 5069
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2009, Volume 2009, Issue 21, pp. 3957 - 3978
In this article we derive a simple twisted relative trace formula. 
MATHEMATICS | INVOLUTIONS | REDUCTIVE GROUPS | REPRESENTATIONS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2007, Volume 135, Issue 8, pp. 2391 - 2401
Let \Gamma\leq\text{SL}_{2}(\mathbb{R}) be a genus zero Fuchsian group of the first kind with \infty as a cusp, and let E_{2k}^{\Gamma} be the holomorphic... 
Zero | Infinity | Inner products | Mathematical constants | Polynomials | Mathematical functions | Mathematical congruence | Fourier coefficients | Mathematical cusps | Divisor polynomials | Eisenstein series | Modular forms | MATHEMATICS | MATHEMATICS, APPLIED | modular forms | divisor polynomials
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 9/2018, Volume 22, Issue 3, pp. 543 - 562
In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands’ beyond endoscopy proposal.... 
05E10 | 11P84 | 11S40 | 05E05 | Mathematics | multiplicities in the plethysm expansion | Combinatorics | partition identities | explicit Satake inversions | MATHEMATICS, APPLIED | REPRESENTATIONS | Endoscopy
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2007, Volume 37, Issue 5, pp. 1593 - 1622
One of the main goals in this paper is to establish convolution sums of functions for the divisor sums "${\tilde \sigma _S}\left( n \right) =... 
Integers | Numbers | Series convergence | Mathematical theorems | Logical proofs | Differential equations | Mathematical functions | Mathematical congruence | Coefficients | MATHEMATICS | 33E05 | 11A67
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 02/2014, Volume 10, Issue 1, pp. 161 - 176
Let E/ℚ be a totally real number field that is Galois over ℚ, and let π be a cuspidal, nondihedral automorphic representation of GL2( E) that is in the lowest... 
Hilbert modular varieties | Algebraic cycles | Tate classes | FORMS | MATHEMATICS | COHOMOLOGY | REPRESENTATIONS | SURFACES
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 277, Issue 1, pp. 99 - 118
In this paper we prove a relative trace formula for all pairs of connected algebraic groups H <= G x G, with G a reductive group and H the direct product of a... 
Relative trace formula | Weyl law | MATHEMATICS | relative trace formula | REPRESENTATIONS
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 2/2008, Volume 15, Issue 2, pp. 235 - 257
In this paper, we define the normalized Eisenstein series ℘, e, and $\mathcal{Q}$ associated with Γ0(2), and derive three differential equations satisfied by... 
Fourier Analysis | Functions of a Complex Variable | Gaussian hypergeometric series | Field Theory and Polynomials | Eisenstein series | Mathematics | Number Theory | Combinatorics | 33C05 | 11F11
Journal Article
12/2019
In this paper, we study the order of the pole of the triple tensor product $L$-functions $L(s,\pi_1\times\pi_2\times\pi_3,\otimes^3)$ for cuspidal automorphic... 
Mathematics - Number Theory
Journal Article
The Ramanujan Journal: An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan, ISSN 1382-4090, 02/2008, Volume 15, Issue 2, p. 235
In this paper, we define the normalized Eisenstein series a, e, and Q associated with I.sub.0(2), and derive three differential equations satisfied by them... 
Journal Article
Research in Number Theory, ISSN 2363-9555, 12/2016, Volume 2, Issue 1, pp. 1 - 12
Langlands’ beyond endoscopy proposal for establishing functoriality motivates the study of irreducible subgroups of $$\mathrm {GL}_n$$ GL n that stabilize a... 
Secondary 20G05 | Mathematics | Primary 11F70 | Number Theory
Journal Article
Acta Arithmetica, ISSN 0065-1036, 2003, Volume 110, Issue 4, pp. 381 - 399
Journal Article
10/2015
Motivated by the Langlands' beyond endoscopy proposal for establishing functoriality, we study the representation $\otimes^3$ in a setting related to the... 
Mathematics - Number Theory
Journal Article
09/2015
Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic... 
Journal Article
07/2015
Rocky Mt. J. Math., Vol 37, No 5 (2007), 315-344 One of the main goals in this paper is to establish convolution sums of functions for the divisor sums... 
Mathematics - Number Theory
Journal Article
07/2015
Int. Math. Res. Not. (IMRN), (2009), 3957-3978 In this article we derive a simple twisted relative trace formula. 
Mathematics - Number Theory
Journal Article
07/2015
Ramanujan J., Vol 15, No 2 (2008), 235-257 In this paper, we define the normalized Eisenstein series $\mathcal{P}$, $e$, and $\mathcal{Q}$ associated with... 
Mathematics - Number Theory
Journal Article
07/2015
Int. J. Number Theory, Vol 10, No 1 (2014), 161-176 Let $E/\mathbb{Q}$ be a totally real number field that is Galois over $\mathbb{Q}$, and let $\pi$ be a... 
Mathematics - Number Theory
Journal Article
06/2014
Pacific J. Math. 277 (2015) 99-118 In this paper, we prove a general simple relative trace formula. As an application, we prove a relative analogue of the Weyl... 
Journal Article
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