اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNon-vanishing of Dirichlet L-functions in Galois orbits
118
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A well known result of Iwaniec and Sarnak states that for at least one third of the primitive Dirichlet characters to a large modulus q, the associated L-functions do not vanish at the central point. When q is a large power of a fixed prime, we prove the same proportion already among the primitive characters of any given order. The set of primitive characters modulo q of a given order can be described as an orbit under the action of the Galois group of the corresponding cyclotomic field. We also prove a positive proportion of nonvanishing within substantially shorter orbits generated by intermediate Galois groups as soon as they are larger than roughly the square-root of the prime-power conductor.
قيم البحث
اقرأ أيضاً
In this paper, we consider the family ${L_j(s)}_{j=1}^{infty}$ of $L$-functions associated to an orthonormal basis ${u_j}_{j=1}^{infty}$ of even Hecke-Maass forms for the modular group $SL(2, Z)$ with eigenvalues ${lambda_j=kappa_{j}^{2}+1/4}_{j=1}^{
infty}$. We prove the following effective non-vanishing result: At least $50 %$ of the central values $L_j(1/2)$ with $kappa_j leq T$ do not vanish as $Trightarrow infty$. Furthermore, we establish effective non-vanishing results in short intervals.
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 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].
Let $qge3$ be an integer, $chi$ be a Dirichlet character modulo $q$, and $L(s,chi)$ denote the Dirichlet $L$-functions corresponding to $chi$. In this paper, we show some special function series, and give some new identities for the Dirichlet $L$-fun
ctions involving Gauss sums. Specially, we give specific identities for $L(2,chi)$.
Let $pi$ be an irreducible cuspidal automorphic representation of a quasi-split unitary group ${rm U}_{mathfrak n}$ defined over a number field $F$. Under the assumption that $pi$ has a generic global Arthur parameter, we establish the non-vanishing
of the central value of $L$-functions, $L(frac{1}{2},pitimeschi)$, with a certain automorphic character $chi$ of ${rm U}_1$, for the case of ${mathfrak n}=2,3,4$, and for the general ${mathfrak n}geq 5$ by assuming a conjecture on certain refined properties of global Arthur packets. In consequence, we obtain some simultaneous non-vanishing results for the central $L$-values by means of the theory of endoscopy.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
