Results 21 to 30 of about 265 (42)
Forum of Mathematics, SigmaThis article presents new rationality results for the ratios of critical values of Rankin–Selberg L-functions of $\mathrm {GL}(n) \times \mathrm {GL}(n')$ over a totally imaginary field $F.$ The proof is based on a cohomological ...
A. Raghuram
doaj +1 more source
The circle method and bounds for $L$-functions - I [PDF]
, 2012 Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid subconvex bound $$ L(1/2+it,
Munshi, Ritabrata
core
On the spinor L-function of Miyawaki-Ikeda lifts
, 2013 We consider lifts from two elliptic modular forms to Siegel modular forms of odd degrees which are special cases of Miyawaki-Ikeda lifts. Assuming non-vanishing of these Miyawaki-Ikeda lifts, we show that the spinor L-functions of these Miyawaki-Ikeda ...
Hayashida, Shuichi
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Shifted convolution sums for $GL(3)\times GL(2)$
, 2012 For the shifted convolution sum $$ D_h(X)=\sum_{m=1}^\infty\lambda_1(1,m)\lambda_2(m+h)V(\frac{m}{X}) $$ where $\lambda_1(1,m)$ are the Fourier coefficients of a $SL(3,\mathbb Z)$ Maass form $\pi_1$, and $\lambda_2(m)$ are those of a $SL(2,\mathbb Z ...
Munshi, Ritabrata
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Bounds for twisted symmetric square $L$-functions - III
, 2012 Let $f$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is an odd prime. In this paper we prove the subconvex bound $$ 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
Dirichlet polynomials, Majorization, and Trumping
, 2013 Majorization and trumping are two partial orders which have proved useful in quantum information theory. We show some relations between these two partial orders and generalized Dirichlet polynomials, Mellin transforms, and completely monotone functions ...
Pereira, Rajesh, Plosker, Sarah
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Varieties via their L-functions
, 2018 We describe a procedure for determining the existence, or non-existence, of an algebraic variety of a given conductor via an analytic calculation involving L-functions.
Farmer, David W. +2 more
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Evaluating $L$-functions with few known coefficients
, 2013 We address the problem of evaluating an $L$-function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that is possible to evaluate the $L$-function more precisely than one ...
Farmer, David W., Ryan, Nathan C.
core +1 more source
Subconvex bounds on GL(3) via degeneration to frequency zero
, 2018 For a fixed cusp form $\pi$ on $\operatorname{GL}_3(\mathbb{Z})$ and a varying Dirichlet character $\chi$ of prime conductor $q$, we prove that the subconvex bound \[ L(\pi \otimes \chi, \tfrac{1}{2}) \ll q^{3/4 - \delta} \] holds for any $\delta < 1/36$.
Holowinsky, Roman, Nelson, Paul D.
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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
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