S. Singh

activity

20162023

most citedt-Aspect Subconvexity Bound for

G L (2)

L-functions

8 citations · 25 across the 15 of their papers we have counts for

collaborators

Showing math.NTShow all

15 papers · 1 filter

math.NT2023★ 2 cited

Sum of the $G L (3)$ Fourier coefficients over mixed powers

Himanshi Chanana, Saurabh Kumar Singh

Let $A (n)$ be the $(1, n)$ -th Fourier coefficients of $S L (3, Z)$ Hecke-Maass cusp form, denoted as $A (1, n)$ or the triple divisor function, denoted as $d_{3} (n)$ . Let $k \geqs…

math.NT2023

Hybrid subconvexity bound for $G L (3) \times G L (2)$ $L$ -functions: t and level aspect

Mohd Harun, Sumit Kumar, Saurabh Kumar Singh

\begin{abstract} In this article, we will get non-trivial estimates for the central values of degree six Rankin-Selberg $L$ -functions $L (1/2 + i t, π \times f)$ associated with a ${GL(…

math.NT2023

Moments of derivatives of modular $L$ -functions

Sumit Kumar, Kummari Mallesham, Prahlad Sharma +1

Let $f$ be an Hecke eigenform for the group $Γ_{0} (q)$ and $χ_{d}$ be a primitive quadratic character of conductor $∣ d ∣$ . In this article, we prove an asymptotic for the second mom…

math.NT2022

Shifted Convolution Sum for $G L (3) \times G L (2)$ with Weighted Average

Mohd Harun, Saurabh Kumar Singh

In this paper, we will prove the non-trivial bound for the weighted average version of shifted convolution sum for $G L (3) \times G L (2)$ , i.e. for any $ε > 0$ and $X^{1/4+δ} \leq H \le…

math.NT2021

Sub-convexity bound for $G L (3) \times G L (2)$ $L$ -functions: Hybrid level aspect

Sumit Kumar, Ritabrata Munshi, Saurabh Kumar Singh

Let $F$ be a $G L (3)$ Hecke-Maass cusp form of prime level $P_{1}$ and let $f$ be a $G L (2)$ Hecke-Maass cuspform of prime level $P_{2}$ . In this article, we will prove a subconvex bou…

math.NT2020

Subconvexity for $G L (3) \times G L (2)$ $L$ -functions in the depth aspect

Sumit Kumar, Kummari Mallesham, Saurabh Kumar Singh

In this article, we will prove subconvex bounds for $G L (3) \times G L (2)$ $L$ -functions in the depth aspect.

math.NT2020★ 5 cited

$t$ -aspect subconvexity for $G L (2) \times G L (2)$ $L$ -function

Ratnadeep Acharya, Prahlad Sharma, Saurabh Kumar Singh

In this paper we shall prove a subconvexity bound for $G L (2) \times G L (2)$ $L$ -function in $t$ -aspect by using a $G L (1)$ circle method.

math.NT2020

Bounds for del Pezzo surfaces of degree two

Aritra Ghosh, Sumit Kumar, Kummari Mallesham +1

In this article, we obtain an upper bound for the number of integral points on the del Pezzo surfaces of degree two.

math.NT2020★ 6 cited

Subconvex bound for $GL(3) \times GL(2)$ $L$ -functions: $GL(3)$ -spectral aspect

Sumit Kumar, Kummari Mallesham, Saurabh Kumar Singh

Let $ϕ$ be a Hecke-Maass cusp form for $SL (3, Z)$ with Langlands parameters $(t_{i})_{i = 1}^{3}$ and $f$ be a holomorphic or Hecke-Maass cusp form for $\math…

math.NT2019

Non-linear additive twist of Fourier coefficients of $G L (3) \times G L (2)$ and $G L (3)$ Maass forms

Sumit Kumar, Kummari Mallesham, Saurabh Kumar Singh

Let $λ_{π} (m, n)$ be the Fourier coefficients of a Hecke-Maass cusp form $π$ for $S L (3, Z)$ and $λ_{f} (n)$ be the Fourier coefficients of Hecke-eigen form $f$ for $SL(2,\mathb…

math.NT2018★ 1 cited

Subconvexity bound for $G L (2)$ L-functions: \lowercase{t}-aspect

Ratnadeep Acharya, Sumit Kumar, Gopal Maiti +1

Let $f$ be a holomorphic Hecke eigenform or a Hecke-Maass cusp form for the full modular group $S L (2, Z)$ . In this paper we shall use circle method to prove the Weyl exp…

math.NT2017★ 1 cited

W\lowercase{eyl} \lowercase {bound for $p$ -power twist of} $G L (2)$ L-\lowercase{functions }

Ritabrata Munshi, Saurabh Kumar Singh

Let $f$ be a cuspidal eigenform (holomorphic or Maass) on the full modular group $S L (2, Z)$ . Let $χ$ be a primitive character of modulus $P$ . We shall prove the following…

math.NT2017★ 8 cited

t-Aspect Subconvexity Bound for $G L (2)$ L-functions

Keshav Aggarwal, Saurabh Kumar Singh

Let $f$ be a holomorphic Hecke eigenforms or a Hecke-Maass cusp form for the full modular group $S L (2, Z)$ . In this paper we shall use circle method to prove the Weyl ex…

math.NT2016

On the Riesz means of $δ_{k} (n)$

Saurabh Kumar Singh

Let $k \geq 1$ be an integer. Let $δ_{k} (n)$ denote the maximum divisor of $n$ which is co-prime to $k$ . We study the error term of the general $m$ -th Riesz mean of the arithmetical f…

math.NT2016★ 2 cited

On double shifted convolution sum of $S L (2, Z)$ Hecke eigen forms

Saurabh Kumar Singh

Let $λ_{i} (n)$ $i = 1, 2, 3$ denote the normalised Fourier coefficients of holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: \[ S:= \frac{1}{H}\sum_{…

Sum of the GL(3) Fourier coefficients over mixed powers

Hybrid subconvexity bound for GL(3)×GL(2) L-functions: t and level aspect

Moments of derivatives of modular L-functions

Shifted Convolution Sum for GL(3)×GL(2) with Weighted Average

Sub-convexity bound for GL(3)×GL(2) L-functions: Hybrid level aspect

Subconvexity for GL(3)×GL(2) L-functions in the depth aspect

t-aspect subconvexity for GL(2)×GL(2) L-function

Bounds for del Pezzo surfaces of degree two

Subconvex bound for GL(3)×GL(2) L-functions: GL(3)-spectral aspect

Non-linear additive twist of Fourier coefficients of GL(3)×GL(2) and GL(3) Maass forms

Subconvexity bound for GL(2) L-functions: \lowercase{t}-aspect

W\lowercase{eyl} \lowercase {bound for p-power twist of} GL(2) L-\lowercase{functions }

t-Aspect Subconvexity Bound for GL(2) L-functions

On the Riesz means of δk​(n)

On double shifted convolution sum of SL(2,Z) Hecke eigen forms

Sum of the $G L (3)$ Fourier coefficients over mixed powers

Hybrid subconvexity bound for $G L (3) \times G L (2)$ $L$ -functions: t and level aspect

Moments of derivatives of modular $L$ -functions

Shifted Convolution Sum for $G L (3) \times G L (2)$ with Weighted Average

Sub-convexity bound for $G L (3) \times G L (2)$ $L$ -functions: Hybrid level aspect

Subconvexity for $G L (3) \times G L (2)$ $L$ -functions in the depth aspect

$t$ -aspect subconvexity for $G L (2) \times G L (2)$ $L$ -function

Subconvex bound for $GL(3) \times GL(2)$ $L$ -functions: $GL(3)$ -spectral aspect

Non-linear additive twist of Fourier coefficients of $G L (3) \times G L (2)$ and $G L (3)$ Maass forms

Subconvexity bound for $G L (2)$ L-functions: \lowercase{t}-aspect

W\lowercase{eyl} \lowercase {bound for $p$ -power twist of} $G L (2)$ L-\lowercase{functions }

t-Aspect Subconvexity Bound for $G L (2)$ L-functions

On the Riesz means of $δ_{k} (n)$

On double shifted convolution sum of $S L (2, Z)$ Hecke eigen forms