Do you want to publish a course? Click here

The shifted fourth moment of automorphic L-functions of prime power level

104   0   0.0 ( 0 )
 Added by Olga Balkanova
 Publication date 2015
  fields
and research's language is English




Ask ChatGPT about the research

We prove the asymptotic formula for the fourth moment of automorphic $L$-functions of level $p^{ u}$, where $p$ is a fixed prime number and $ u rightarrow infty$. This paper is a continuation of work by Rouymi, who computed asymptotics of the first three moments at prime power level, and a generalization of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.



rate research

Read More

183 - Thomas A. Hulse 2013
In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic cusp forms. The foundations of this construction are based in the continuation of the spectral expansion of a special truncated Poincare series recently developed by Jeffrey Hoffstein. As a result we are able to produce previously unstudied and nontrivial asymptotics of truncated shifted sums which we expect to correspond to off-diagonal terms in the third moment of automorphic 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 arguments of Soundararajan and Young [19] and Soundararajan [17].
93 - Nikolaos Diamantis 2016
We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Browns technique to study multiple modular values with the properties of a double Eisentein series previously studied by the author and C. OSullivan.
The moments of quadratic Dirichlet $L$-functions over function fields have recently attracted much attention with the work of Andrade and Keating. In this article, we establish lower bounds for the mean values of the product of quadratic Dirichlet $L$-functions associated with hyperelliptic curves of genus $g$ over a fixed finite field $mathbb{F}_q$ in the large genus limit. By using the idea of A. Florea cite{FL3}, we also obtain their upper bounds. As a consequence, we find upper bounds of its derivatives. These lower and upper bounds give the correlation of quadratic Dirichlet $L$-functions associated with hyperelliptic curves with different transitions.
412 - 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.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا