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Ritabrata Munshi

Publications and source records attributed to Ritabrata Munshi.

28 records · Page 2Linked to original sources
arXiv2014

Hybrid subconvexity bounds for $L \left(\tfrac{1}{2}, \text{Sym}^2 f \otimes g\right)$

Fix an integer $κ\geqslant 2$. Let $P$ be prime and let $k> κ$ be an even integer. For $f$ a holomorphic cusp form of weight $k$ and full level and $g$ a primitive holomorphic cusp form of weight $2 κ$ and level $P$, we prove hybrid subconvexity bounds for $L \left(\tfrac{1}{2}, \text{Sym}^2 f \otimes g\right)$ in the $k$ and $P$ aspects when $P^{\frac {13} {64} + δ} < k < P^{\frac 3 8 - δ}$ for any $0 < δ< \frac {11} {128}$. These bounds are achieved through a first moment method (with amplification when $P^{\frac {13} {64}} < k \leqslant P^{\frac 4 {13}}$).

math.NT↗
arXiv2012

Bounds for twisted symmetric square $L$-functions - III

Let $f$ be a newform, and let $χ$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is an odd prime. In this paper we prove the subconvex bound $$ L(\t1/2,\Sym f\otimesχ)\ll_{f,q,\varepsilon} q^{3\ell(1/4-1/36+\varepsilon)} $$ for any $\varepsilon>0$. This can be compared with the recently established $t$-aspect subconvexity of the symmetric square $L$-functions.

math.NT↗
arXiv2012

Level Aspect Subconvexity For Rankin-Selberg $L$-functions

Let $M$ be a square-free integer and let $P$ be a prime not dividing $M$ such that $P \sim M^η$ with $0<η<2/21$. We prove subconvexity bounds for $L(\tfrac{1}{2}, f \otimes g)$ when $f$ and $g$ are two primitive holomorphic cusp forms of levels $P$ and $M$. These bounds are achieved through an unamplified second moment method.

math.NT↗
arXiv2012

Bounds for twisted symmetric square $L$-functions

Let $f\in S_k(N,ψ)$ be a newform, and let $χ$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is a prime and $\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form $$ L(\tfrac{1}{2},\Sym f\otimesχ)\ll_{f,\varepsilon} q^{3/4\ell-δ_{\ell}+\varepsilon} $$ for some $δ_{\ell}>0$ and any $\varepsilon>0$. In particular, for $\ell=3$ we show that the bound holds with $δ_{\ell}=1/4$.

math.NT↗
arXiv2012

The circle method and bounds for $L$-functions - I

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $χ$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes χ)$ we establish the hybrid subconvex bound $$ L(1/2+it,f\otimesχ)\ll (M(3+|t|))^{1/2-1/18+\varepsilon}, $$ for $t\in \mathbb R$. The implied constant depends only on the form $f$ and $\varepsilon$.

math.NT↗
arXiv2012

Shifted convolution sums for $GL(3)\times GL(2)$

For the shifted convolution sum $$ D_h(X)=\sum_{m=1}^\inftyλ_1(1,m)λ_2(m+h)V(\frac{m}{X}) $$ where $λ_1(1,m)$ are the Fourier coefficients of a $SL(3,\mathbb Z)$ Maass form $π_1$, and $λ_2(m)$ are those of a $SL(2,\mathbb Z)$ Maass or holomorphic form $π_2$, and $1\leq |h| \ll X^{1+\varepsilon}$, we establish the bound $$ D_h(X)\ll_{π_1,π_2,\varepsilon} X^{1-(1/20)+\varepsilon}. $$ The bound is uniform with respect to the shift $h$.

math.NT↗