Bounds for twisted symmetric square $L$-functions
, 2012 Let $f\in S_k(N,\psi)$ be a newform, and let $\chi$ 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 $$ L(\tfrac{1}{2},\Sym f ...
Munshi, Ritabrata
core +1 more source
Bounds for twisted symmetric square $L$-functions - III
, 2012 Let $f$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is an odd prime. In this paper we prove the subconvex bound $$ L(\t1/2,\Sym f\otimes\chi)\ll_{f,q,\varepsilon} q^{3\ell(1/4-1/36+\varepsilon)} $$ for ...
Blomer +8 more
core +1 more source
Shifted convolution sums for $GL(3)\times GL(2)$
, 2012 For the shifted convolution sum $$ D_h(X)=\sum_{m=1}^\infty\lambda_1(1,m)\lambda_2(m+h)V(\frac{m}{X}) $$ where $\lambda_1(1,m)$ are the Fourier coefficients of a $SL(3,\mathbb Z)$ Maass form $\pi_1$, and $\lambda_2(m)$ are those of a $SL(2,\mathbb Z ...
Munshi, Ritabrata
core +1 more source
Improved subconvexity bounds for GL(2)xGL(3) and GL(3) L-functions by weighted stationary phase
, 2017 Let $f$ be a fixed self-contragradient Hecke-Maass form for $SL(3,\mathbb Z)$, and $u$ an even Hecke-Maass form for $SL(2,\mathbb Z)$ with Laplace eigenvalue $1/4+k^2$, $k>0$. A subconvexity bound $O\big(k^{4/3+\varepsilon}\big)$ in the eigenvalue aspect
McKee, Mark, Sun, Haiwei, Ye, Yangbo
core +1 more source
Regulator proofs for Boyd's identities on genus 2 curves
, 2018 We use the elliptic regulator to recover some identities between Mahler measures involving certain families of genus 2 curves that were conjectured by Boyd and proven by Bertin and Zudilin by differentiating the Mahler measures and using hypergeometric ...
Lalín, Matilde, Wu, Gang
core +1 more source
Simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass L-functions
, 2014 We prove that given a Hecke-Maass form $f$ for $\text{SL}(2, \mathbb{Z})$ and a sufficiently large prime $q$, there exists a primitive Dirichlet character $\chi$ of conductor $q$ such that the $L$-values $L(\tfrac{1}{2}, f \otimes \chi)$ and $L(\tfrac{1}{
Das, Soumya, Khan, Rizwanur
core
Applications of the Kuznetsov formula on GL(3). [PDF]
Invent Math, 2013 Blomer V.
europepmc +1 more source
Assignment of groups responsible for the "opsin shift" and light absorptions of rhodopsin and red, green, and blue iodopsins (cone pigments). [PDF]
Proc Natl Acad Sci U S A, 1988 Kosower EM.
europepmc +1 more source
The metabolism of tryptophan: The mode of formation of kynurenic acid from tryptophan. [PDF]
Biochem J, 1928 Robson W.
europepmc +1 more source
Mean values connected with the Dedekind zeta-function of a non-normal cubic field
Open Mathematics, 2013 Lü Guangshi
doaj +1 more source