Related papers: Formule de Trace pour le Anneaux de Witt

We study exponential sums on Witt vectors, known as Gauss--Heilbronn sums, and the curves whose Frobenius traces realize these sums via a Deligne--Lusztig type construction. For 3-typical Witt vectors of length two, we analyze…

Our main goal in this paper is to prove results for Witt vectors in the almost category. We finish with an application to almost purity, in particular offering a new proof for rank one valuation rings.

We give a formula for matrix exponentials and partial fraction decompositions.

We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…

We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of…

We define the resultant of two power series with coefficients in the ring of integers of a $p$-adic field. In order to do this, we prove a universal version of the Weierstrass preparation theorem.

We provide numerical procedures for possibly best evaluating the sum of positive series. Our procedures are based on the application of a generalized version of Kummer's test.

Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.

The theme of the article is the study of the unipotent part of Arthur's trace formula for general linear groups. The case of regular (or "regular by blocks") unipotent orbits has been essentially done in a previous paper. Here we are…

We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.

We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.

There exist several equivalent equations for the Poincar\'e series of a collection of valuations on the ring of germs of functions on a complex analytic variety. We give definitions of the Poinca\'e series of a collection of valuations in…

In this work we shall generalize the Selberg trace formula to a non-unitary finite-dimensional complex representation $\chi:\Gamma\rightarrow\operatorname{GL}(V)$ of a uniform lattice $\Gamma$ of a real Lie group $G$.

Improving and extending recent results of the author, we conditionally estimate exponential sums with Dirichlet coefficients of L-functions, both over all integers and over all primes in an interval. In particular, we establish new…

The main goal of this paper is to compute the characteristic class of the Alekseev-Lachowska *-product on coadjoint orbits. We deduce an analogue of the Weyl dimension formula in the context of deformation quantization.

This paper introduces the target sum function along with its characteristics. The target sum function takes a list of integers and a specific target integer as input values and expresses the number of ways to obtain the target sum by either…

The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…

A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…

We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable…

Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently…