Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSimultaneous nonvanishing of the Products of L-functions associated to elliptic cusp forms
90
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A generalized Riemann hypothesis states that all zeros of the completed Hecke $L$-function $L^*(f,s)$ of a normalized Hecke eigenform $f$ on the full modular group should lie on the vertical line $Re(s)=frac{k}{2}.$ It was shown by Kohnen that there exists a Hecke eigenform $f$ of weight $k$ such that $L^*(f,s) eq 0$ for sufficiently large $k$ and any point on the line segments $Im(s)=t_0, frac{k-1}{2} < Re(s) < frac{k}{2}-epsilon, frac{k }{2}+epsilon < Re(s) < frac{k+1}{2},$ for any given real number $t_0$ and a positive real number $epsilon.$ This paper concerns the non-vanishing of the product $L^*(f,s)L^*(f,w)$ $(s,win mathbb{C})$ on average.
rate research
Read More
We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing invaria
We define L-functions for the class of real-analytic modular forms recently introduced by F. Brown. We establish their main properties and construct the analogue of period polynomial in cases of special interest, including those of modular iterated integrals.
A conjecture of Le says that the Deligne polytope $Delta_d$ is generically ordinary if $pequiv 1 (!!bmod D(Delta_d))$, where $D(Delta_d)$ is a combinatorial constant determined by $Delta_d$. In this paper a counterexample is given to show that the conjecture is not true in general.
In recent years, a number of papers have been devoted to the study of roots of period polynomials of modular forms. Here, we study cohomological analogues of the Eichler-Shimura period polynomials corresponding to higher $L$-derivatives. We state general conjectures about the locations of the roots of the full and odd parts of the polynomials, in analogy with the existing literature on period polynomials, and we also give numerical evidence that similar results hold for our higher derivative period polynomials in the case of cusp forms. We prove a special case of this conjecture in the case of Eisenstein series.
We study the asymptotic behaviour of the twisted first moment of central $L$-values associated to cusp forms in weight aspect on average. Our estimate of the error term allows extending the logarithmic length of mollifier $Delta$ up to 2. The best previously known result, due to Iwaniec and Sarnak, was $Delta<1$. The proof is based on a representation formula for the error in terms of Legendre polynomials.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
