Neha Prabhu

activity

20162023

most citedThe error term in the Sato-Tate theorem of Birch

3 citations · 4 across the 5 of their papers we have counts for

collaborators

8 papers

math.NT2023

A central limit theorem for Hilbert modular forms

Jishu Das, Neha Prabhu

For a prime ideal $p$ in a totally real number field $L$ with the adele ring $A$ , we study the distribution of angles $θ_{π} (p)$ coming from Satake par…

math.NT2020

Equidistribution of $α p^{θ}$ with a Chebotarev condition and applications to extremal primes

Amita Malik, Neha Prabhu

We establish a joint distribution result concerning the fractional part of $α p^{θ}$ for $θ \in (0, 1), α > 0$ , where $p$ is a prime satisfying a Chebotarev condition in a fixed finite…

math.NT2019★ 3 cited

The error term in the Sato-Tate theorem of Birch

M. Ram Murty, Neha Prabhu

We establish an error term in the Sato-Tate theorem of Birch. That is, for $p$ prime, $q = p^{r}$ we show that $\#\{ (a,b) \in \mathbb{F}_q^2 : θ_{a,b}\in I\} =μ_{ST}(I)q^2 + O_r(q^{7/…

math.NT2019

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

Stephan Baier, Neha Prabhu, Kaneenika Sinha

The second and third-named authors (arXiv:1705.04115) established a Central Limit Theorem for the error term in the Sato-Tate law for families of modular forms. This method was ada…

math.NT2018★ 1 cited

Extremal primes of elliptic curves without complex multiplication

C. David, A. Gafni, A. Malik +2

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to th…

math.NT2017

Moments of the error term in the Sato-Tate law for elliptic curves

Stephan Baier, Neha Prabhu

We derive new bounds for moments of the error in the Sato-Tate law over families of elliptic curves. Our estimates are stronger than those obtained by W.D. Banks and I.E. Shparlins…

math.NT2017

Fluctuations in the distribution of Hecke eigenvalues about the Sato-Tate measure

Neha Prabhu, Kaneenika Sinha

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(\ma…

math.NT2016

Density of solutions to quadratic congruences