ترغب بنشر مسار تعليمي؟ اضغط هنا

The first moment of quadratic twists of modular $L$-functions

130   0   0.0 ( 0 )
 نشر من قبل Quanli Shen
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Quanli Shen




اسأل ChatGPT حول البحث

We obtain the asymptotic formula with an error term $O(X^{frac{1}{2} + varepsilon})$ for the smoothed first moment of quadratic twists of modular $L$-functions. We also give a similar result for the smoothed first moment of the first derivative of quadratic twists of modular $L$-functions. The argument is largely based on Youngs recursive method [19,20].



قيم البحث

اقرأ أيضاً

423 - Matthew P. Young 2008
We obtain an asymptotic formula for the smoothly weighted first moment of primitive quadratic Dirichlet L-functions at the central point, with an error term that is square-root of the main term. Our approach uses a recursive technique that feeds the result back into itself, successively improving the error term.
We prove an asymptotic formula with a power saving error term for the (pure or mixed) second moment of central values of L-functions of any two (possibly equal) fixed cusp forms f, g twisted by all primitive characters modulo q, valid for all suffici ently factorable q including 99.9% of all admissible moduli. The two key ingredients are a careful spectral analysis of a potentially highly unbalanced shifted convolution problem in Hecke eigenvalues and power-saving bounds for sums of products of Kloosterman sums where the length of the sum is below the square-root threshold of the modulus. Applications are given to simultaneous non-vanishing and lower bounds on higher moments of twisted L-functions.
66 - Quanli Shen 2019
We study the fourth moment of quadratic Dirichlet $L$-functions at $s= frac{1}{2}$. We show an asymptotic formula under the generalized Riemann hypothesis, and obtain a precise lower bound unconditionally. The proofs of these results follow closely a rguments of Soundararajan and Young [19] and Soundararajan [17].
109 - Olga Balkanova 2019
We prove an asymptotic formula for the twisted first moment of Maass form symmetric square L-functions on the critical line and at the critical point. The error term is estimated uniformly with respect to all parameters.
We calculate certain wide moments of central values of Rankin--Selberg $L$-functions $L(piotimes Omega, 1/2)$ where $pi$ is a cuspidal automorphic representation of $mathrm{GL}_2$ over $mathbb{Q}$ and $Omega$ is a Hecke character (of conductor $1$) o f an imaginary quadratic field. This moment calculation is applied to obtain weak simultaneous non-vanishing results, which are non-vanishing results for different Rankin--Selberg $L$-functions where the product of the twists is trivial. The proof relies on relating the wide moments to the usual moments of automorphic forms evaluated at Heegner points using Waldspurgers formula. To achieve this, a classical version of Waldspurgers formula for general weight automorphic forms is proven, which might be of independent interest. A key input is equidistribution of Heegner points (with explicit error-terms) together with non-vanishing results for certain period integrals. In particular, we develop a soft technique for obtaining non-vanishing of triple convolution $L$-functions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا