ترغب بنشر مسار تعليمي؟ اضغط هنا

Moments and hybrid subconvexity for symmetric-square L-functions

84   0   0.0 ( 0 )
 نشر من قبل Rizwanur Khan
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We establish sharp bounds for the second moment of symmetric-square $L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$, where the second moment is a sum over $t_j$ in a short interval. At the central point $s=1/2$ of the $L$-function, our interval is smaller than previous known results. More specifically, for $|t_j|$ of size $T$, our interval is of size $T^{1/5}$, while the previous best was $T^{1/3}$ from work of Lam. A little higher up on the critical line, our second moment yields a subconvexity bound for the symmetric-square $L$-function. More specifically, we get subconvexity at $s=1/2+it$ provided $|t_j|^{6/7+delta}le |t| le (2-delta)|t_j|$ for any fixed $delta>0$. Since $|t|$ can be taken significantly smaller than $|t_j|$, this may be viewed as an approximation to the notorious subconvexity problem for the symmetric-square $L$-function in the spectral aspect at $s=1/2$.



قيم البحث

اقرأ أيضاً

118 - Olga Balkanova 2020
We prove a spectral decomposition formula for averages of Zagier L-series in terms of moments of symmetric square L-functions associated to Maass and holomorphic cusp forms of levels 4, 16, 64.
In this paper we prove a hybrid subconvexity bound for class group $L$-functions associated to a quadratic extension $K/mathbb{Q}$ (real or imaginary). Our proof relies on relating the class group $L$-functions to Eisenstein series evaluated at Heegn er points using formulas due to Hecke. The main technical contribution is the following uniform sup norm bound for Eisenstein series $E(z,1/2+it)ll_varepsilon y^{1/2} (|t|+1)^{1/3+varepsilon}, ygg 1$, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.
Let $f $ be a holomorphic Hecke eigenforms or a Hecke-Maass cusp form for the full modular group $ SL(2, mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that [ L left( fra c{1}{2} + it right) ll_{f, epsilon} left( 1 + |t|right)^{1/3 + epsilon}, ] for any $epsilon > 0.$
Let $f $ be a holomorphic Hecke eigenform or a Hecke-Maass cusp form for the full modular group $ SL(2, mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that [ L left( frac {1}{2} + it, f right) ll_{f, epsilon} left( 2 + |t|right)^{1/3 + epsilon}, ] for any $epsilon > 0.$
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.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا