The Quantitative Distribution of Hecke eigenvalues

Wang, Yingnan

doi:10.1017/s0004972714000070

Cited by 6 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nagoshi [16] obtained the same asymptotic under weaker conditions on the growth of k, namely, k = k(x) satisfies log k log x → ∞ as x → ∞. An effective version of Nagoshi's theorem was proved by Wang [22]. Under the above mentioned conditions, he proves that…”

Section: Introductionmentioning

confidence: 89%

“…An effective version of Nagoshi's theorem was proved by Wang [22]. Under the above mentioned conditions, he proves that…”

Section: Introductionmentioning

confidence: 97%

“…These polynomials were used by M.R. Murty and Sinha [15] and by Wang [22] to obtain error terms in families (B) and (C) respectively. In this article, we use this technique in a more refined way: we compute moments of functions arising from the Beurling-Selberg polynomials which give approximations to higher moments of N I (f, x) − π(x)µ ∞ (I).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fluctuations in the Distribution of Hecke Eigenvalues about the Sato–Tate Measure

Prabhu

Sinha

2017

International Mathematics Research Notices

View full text Add to dashboard Cite

We study fluctuations in the distribution of families of p-th Fourier coefficients a f (p) of normalised holomorphic Hecke eigenforms f of weight k with respect to SL 2 (Z) as k → ∞ and primes p → ∞. These families are known to be equidistributed with respect to the Sato-Tate measure. We consider a fixed interval I ⊂ [−2, 2] and derive the variance of the number of a f (p)'s lying in I as p → ∞ and k → ∞ (at a suitably fast rate). The number of a f (p)'s lying in I is shown to asymptotically follow a Gaussian distribution when appropriately normalised. A similar theorem is obtained for primitive Maass cusp forms.

show abstract

Section: Introductionmentioning

confidence: 89%

“…An effective version of Nagoshi's theorem was proved by Wang [22]. Under the above mentioned conditions, he proves that…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fluctuations in the Distribution of Hecke Eigenvalues about the Sato–Tate Measure

Prabhu

Sinha

2017

International Mathematics Research Notices

View full text Add to dashboard Cite

show abstract

“…for any f ∈ F N,k . By the work of Wang [Wan14], we now have the following unconditional average estimate for the error terms of…”

Section: Introductionmentioning

confidence: 99%

Central limit theorems for elliptic curves and modular forms with smooth weight functions

Baier

Prabhu

Sinha

2020

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

In [PS17], the second and third-named authors established a Central Limit Theorem for the error term in the Sato-Tate law for families of modular forms. This method was adapted to families of elliptic curves in [BP19] by the first and second-named authors. In this context, a Central Limit Theorem was established only under a strong hypothesis going beyond the Riemann Hypothesis. In the present paper, we consider a smoothed version of the Sato-Tate conjecture, which allows us to overcome several limitations. In particular, for the smoothed version, we are able to establish a Central Limit Theorem for much smaller families of modular forms, and we succeed in proving a theorem of this type for families of elliptic curves under the Riemann Hypothesis for L-functions associated to Hecke eigenforms for the full modular group.

show abstract

Some notes on distribution of Hecke eigenvalues for Maass cusp forms

Wang

Xiao

2017

Lith Math J

View full text Add to dashboard Cite

The Quantitative Distribution of Hecke eigenvalues

Abstract: We give two results concerning the distribution of Hecke eigenval-ues of SL(2, Z). The first result asserts that on certain average the Sato-Tate conjecture holds. The second result deals with the Gaussian central limit theorem for Hecke eigenvalues.

Cited by 6 publications

References 9 publications

Fluctuations in the Distribution of Hecke Eigenvalues about the Sato–Tate Measure

Fluctuations in the Distribution of Hecke Eigenvalues about the Sato–Tate Measure

Central limit theorems for elliptic curves and modular forms with smooth weight functions

Some notes on distribution of Hecke eigenvalues for Maass cusp forms

Contact Info

Product

Resources

About