Related papers: $L$-functions of Kloosterman sheaves

Given a perfect field of exponential characteristic $e$ and a functor $f:\mathcal A\to\mathcal B$ between symmetric monoidal strict $V$-categories of correspondences satisfying the cancellation property such that the induced morphisms of…

Thanks to Hrushovski-Loeser's work on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom-Sebastiani theorem in the case of regular functions. Moreover, slightly extending of Hrushovski-Loeser's construction adjusted…

We consider arbitrary algebraic families of lower order deformations of nondegenerate toric exponential sums over a finite field. We construct a relative polytope with the aid of which we define a ring of coefficients consisting of p-adic…

We establish power-saving estimates for general bilinear forms with Kloosterman sums modulo arbitrary q, including when both variables are shorter than the Polya-Vinogradov range. As an application, we obtain power-saving asymptotics for…

We show that integral monodromy groups of Kloosterman $\ell$-adic sheaves of rank $n\ge 2$ on $\mathbb{G}_m/\mathbb{F}_q$ are as large as possible when the characteristic $\ell$ is large enough, depending only on the rank. This variant of…

We define motivic Milnor fiber of cyclic $L_\infty$-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor…

We define L-functions for meromorphic modular forms that are regular at cusps, and use them to: (i) find new relationships between Hurwitz class numbers and traces of singular moduli, (ii) establish predictions from the physics of…

Kloosterman sums for a finite field arise as Frobenius trace functions of certain local systems defined over $\Gm$. The moments of Kloosterman sums calculate the Frobenius traces on the cohomology of tensor powers (or symmetric powers,…

In this thesis we give two applications of Ayoub's motivic nearby cycles functor: First we give a generalization of Grothendieck's classical local monodromy theorem. In the classical setup we show that the inertia group acts…

We define a theory of etale motives over a noetherian scheme. This provides a system of categories of complexes of motivic sheaves with integral coefficients which is closed under the six operations of Grothendieck. The rational part of…

Deligne constructed a remarkable local system on $\bP^1-\{0,\infty\}$ attached to a family of Kloosterman sums. Katz calculated its monodromy and asked whether there are Kloosterman sheaves for general reductive groups and which automorphic…

We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in…

In this article we further the study of non-commutative motives. Our main result is the construction of a symmetric monoidal structure on the localizing motivator Mot of dg categories. As an application, we obtain : (1) a computation of the…

The symmetric power L-function of the hyper-Kloosterman family is a rational function over the integers. Its degree and complex absolute values of its zeros and poles are now known through the work of Fu and Wan. The purpose of this paper…

This article is the first one of a series of three articles devoted to L-functions. In this one we give a definition of the L-functions of convergent or overconvergent F-modules with the help of Teichm\"uller liftings and we establish the…

We study motivic zeta functions of degenerating families of Calabi-Yau varieties. Our main result says that they satisfy an analog of Igusa's monodromy conjecture if the family has a so-called Galois-equivariant Kulikov model; we provide…

We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums, as their parameter varies modulo a prime tending to infinity. Using independence of Kloosterman sheaves, we prove convergence in the…

We construct motivic cohomology classes attached to Rankin--Selberg convolutions of modular forms of weights $\ge 2$, show that these vary analytically in p-adic families, and relate their image under the p-adic regulator map to values of…

In this article we introduce and study a motivic category in the arithmetic of function fields, namely the category of motives over an algebraic closure $L$ of a finite field with coefficients in a global function field over this finite…

Motivic Serre invariants defined by Loeser and Sebag are elements of the Grothendieck ring of varities modulo $\mathbb{L}-1$. In this paper, we show that we can lift these invariants to modulo the square of $\mathbb{L}-1$ after tensoring…