ترغب بنشر مسار تعليمي؟ اضغط هنا

Kernels of L-functions and shifted convolutions

94   0   0.0 ( 0 )
 نشر من قبل Nikolaos Diamantis
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

188 - 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.
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.
106 - Olga Balkanova 2015
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 t hree moments at prime power level, and a generalization of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.
In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved.
We study the average of the product of the central values of two $L$-functions of modular forms $f$ and $g$ twisted by Dirichlet characters to a large prime modulus $q$. As our principal tools, we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of $q$, and we use the theory of Deligne and Katz to estimate certain complete exponential sums in several variables and prove new bounds on bilinear forms in Kloosterman sums with power savings when both variables are near the square root of $q$. When at least one of the forms $f$ and $g$ is non-cuspidal, we obtain an asymptotic formula for the mixed second moment of twisted $L$-functions with a power saving error term. In particular, when both are non-cuspidal, this gives a significant improvement on M.~Youngs asymptotic evaluation of the fourth moment of Dirichlet $L$-functions. In the general case, the asymptotic formula with a power saving is proved under a conjectural estimate for certain bilinear forms in Kloosterman sums.
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