ترغب بنشر مسار تعليمي؟ اضغط هنا

Sums of Kloosterman sums in the prime geodesic theorem

72   0   0.0 ( 0 )
 نشر من قبل Olga Balkanova
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.



قيم البحث

اقرأ أيضاً

Let $Gamma=PSL(2,Z[i])$ be the Picard group and $H^3$ be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient $Gamma setminus H^3$, called the Picard manifold, obtaining an error term of size $O(X^{3/2+theta/2+ epsilon})$, where $theta$ denotes a subconvexity exponent for quadratic Dirichlet $L$-functions defined over Gaussian integers.
We revisit a recent bound of I. Shparlinski and T. P. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earl ier results on sums of Kloosterman sums along the primes and on the error term of the fourth moment of Dirichlet $L$-functions.
138 - Chunlin Wang , Liping Yang 2021
In this paper, we study the Newton polygons for the $L$-functions of $n$-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon. In order to determine the Hodge polygon, we explici tly construct a basis of the top dimensional Dwork cohomology. Using Wans decomposition theorem and diagonal local theory, we obtain when the Newton polygon coincides with the Hodge polygon. In particular, we concretely get the slope sequence for $L$-function of $bar{F}(bar{lambda},x):=sum_{i=1}^nx_i^{a_i}+bar{lambda}prod_{i=1}^nx_i^{-1}$.
198 - Chunlin Wang , Liping Yang 2020
In this paper, we focus on a family of generalized Kloosterman sums over the torus. With a few changes to Haessig and Sperbers construction, we derive some relative $p$-adic cohomologies corresponding to the $L$-functions. We present explicit forms o f bases of top dimensional cohomology spaces, so to obtain a concrete method to compute lower bounds of Newton polygons of the $L$-functions. Using the theory of GKZ system, we derive the Dworks deformation equation for our family. Furthermore, with the help of Dworks dual theory and deformation theory, the strong Frobenius structure of this equation is established. Our work adds some new evidences for Dworks conjecture.
190 - Simon Griffiths 2010
A $k$-sum of a set $Asubseteq mathbb{Z}$ is an integer that may be expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of the number of $(k+1)$-sums to the number of $k$-sums be? Writing $kwedge A$ for the set of $k$-sums of $ A$ we prove that [ frac{|(k+1)wedge A|}{|kwedge A|}, le , frac{|A|-k}{k+1} ] whenever $|A|ge (k^{2}+7k)/2$. The inequality is tight -- the above ratio being attained when $A$ is a geometric progression. This answers a question of Ruzsa.
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