Symmetric power functoriality for holomorphic modular forms
J Newton, JA Thorne - Publications mathématiques de l'IHÉS, 2021 - Springer
Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …
On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motives
Y Liu, Y Tian, L Xiao, W Zhang, X Zhu - Inventiones mathematicae, 2022 - Springer
In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to
Rankin–Selberg products of conjugate self-dual automorphic representations, within the …
Rankin–Selberg products of conjugate self-dual automorphic representations, within the …
From sum of two squares to arithmetic Siegel–Weil formulas
C Li - Bulletin of the American Mathematical Society, 2023 - ams.org
The main goal of this expository article is to survey recent progress on the arithmetic Siegel–
Weil formula and its applications. We begin with the classical sum of two squares problem …
Weil formula and its applications. We begin with the classical sum of two squares problem …
The average behaviour of Hecke eigenvalues over certain sparse sequence of positive integers
G Hua - Research in Number Theory, 2022 - Springer
Let j≥ 2 be a given integer. Let f be a normalized primitive holomorphic cusp form of even
integral weight for the full modular group Γ= SL (2, Z). Denote by λ sym jf (n) the n th …
integral weight for the full modular group Γ= SL (2, Z). Denote by λ sym jf (n) the n th …
Equidistribution of Kloosterman sums over function fields
L Fu, YK Lau, WCW Li, P Xi - arXiv preprint arXiv:2406.10106, 2024 - arxiv.org
arXiv:2406.10106v1 [math.NT] 14 Jun 2024 Page 1 arXiv:2406.10106v1 [math.NT] 14 Jun 2024
EQUIDISTRIBUTION OF KLOOSTERMAN SUMS OVER FUNCTION FIELDS LEI FU, YUK-KAM …
EQUIDISTRIBUTION OF KLOOSTERMAN SUMS OVER FUNCTION FIELDS LEI FU, YUK-KAM …
On the vanishing of adjoint Bloch--Kato Selmer groups of irreducible automorphic Galois representations
JA Thorne - arXiv preprint arXiv:2207.04925, 2022 - arxiv.org
Let $\rho $ be the $ p $-adic Galois representation attached to a cuspidal, regular algebraic,
polarizable automorphic representation of $ GL_n $. Assuming only that $\rho $ satisfies an …
polarizable automorphic representation of $ GL_n $. Assuming only that $\rho $ satisfies an …
On certain kernel functions and shifted convolution sums of the Fourier coefficients
K Venkatasubbareddy, A Sankaranarayanan - Journal of Number Theory, 2024 - Elsevier
On certain kernel functions and shifted convolution sums of the Fourier coefficients -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
The second moment of the Fourier coefficients of triple product L-functions
H Liu - Proceedings-Mathematical Sciences, 2023 - Springer
Suppose that H∗ is the set of all primitive cusp forms f of even integral weight k≥ 2 for the
full modular group SL 2 (Z). In this paper, we establish asymptotic formulas for the second …
full modular group SL 2 (Z). In this paper, we establish asymptotic formulas for the second …
Non-abelian base change for symmetric power liftings of holomorphic modular forms
L Clozel, J Newton, JA Thorne - arXiv preprint arXiv:2312.01774, 2023 - arxiv.org
Let $ f $ be a non-CM Hecke eigenform of weight $ k\geq 2$. We give a new proof of some
cases of Langlands functoriality for the automorphic representation $\pi $ associated to $ f …
cases of Langlands functoriality for the automorphic representation $\pi $ associated to $ f …
On the average behavior of the Fourier coefficients of jth symmetric power L-function over certain sequences of positive integers
A Sharma, A Sankaranarayanan - Czechoslovak Mathematical Journal, 2023 - Springer
We investigate the average behavior of the n th normalized Fourier coefficients of the j th (j≽
2 be any fixed integer) symmetric power L-function (ie, L (s, sym jf)), attached to a primitive …
2 be any fixed integer) symmetric power L-function (ie, L (s, sym jf)), attached to a primitive …