Related papers: p-adic variation of unit root L-functions

As a consequence of Wan's theorem about Dwork's conjecture, the unit root $L$-functions of the $n$-dimensional Kloosterman family are $p$-adic meromorphic. By studying the symmetric power $L$-functions associated to the Kloosterman family,…

Adolphson and Sperber characterized the unique unit root of $L$-function associated with toric exponential sums in terms of the $\mathcal{A}$-hypergeometric functions. For the unit root $L$-function associated with a family of toric…

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

The L-function of symmetric powers of classical Kloosterman sums is a polynomial whose degree is now known, as well as the complex absolute values of the roots. In this paper, we provide estimates for the p-adic absolute values of these…

Wan proved the rationality of partial toric $L$-functions using $\ell$-adic techniques. In this paper, we present a $p$-adic proof in the spirit of Dwork. We demonstrate that partial $L$-functions can be expressed as an alternating product…

Starting from a classical generating series for Bessel functions due to Schlomilch, we use Dwork's relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In…

This is an expository paper which gives a quick introduction to Dwork's conjecture about p-adic meromorphic continuation of his unit root zeta function arising from algebraic geometry. Special emphasis is given to the case of elliptic…

We demonstrate that Wan's alternate description of Dwork's unit root L-function in the rank one case may be modified to give a proof of meromorphy that is classical, eliminating the need to study sequences of uniform meromorphic functions.

In this paper, we focus on a family of generalized Kloosterman sums over the torus. With a few changes to Haessig and Sperber's construction, we derive some relative $p$-adic cohomologies corresponding to the $L$-functions. We present…

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…

In this article, we introduce a systematic new method to investigate the conjectural p-adic meromorphic continuation of Professor Bernard Dwork's unit root zeta function attached to an ordinary family of algebraic varieties defined over a…

For \psi a nontrivial additive character on the finite field F_q, the map t \mapsto \sum_{x \in F_q} \psi(f(x)+tx) is the Fourier transform of the map t \mapsto \psi(f(t))$. As is well-known, this has a cohomological interpretation,…

A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this article we prove results in this vein for the ordinary part…

We construct examples of p-adic L-functions over universal deformation spaces for GL(2). We formulate a conjecture predicting that the natural parameter spaces for p-adic L-functions are not the usual eigenvarieties (parametrising…

For each positive integer k, we investigate the L-function attached to the k-th symmetric power of the F-crystal associated to the family of cubic exponential sums of x^3 + \lambda x. We explore its rationality, field of definition, degree,…

The infinity symmetric power $L$-functions play a fundamental role in Wan's groundbreaking work on Dwork's conjecture[16]. Building upon this foundation, Haessig[8] established the $p$-adic estimates for these $L$-functions in the case of…

We define a p-adic character to be a continuous homomorphism from 1 + t\Fq[[t]] to \Zp^*. We use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (c_i) of elements in Zq, indexed by natural…

We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity…

In this paper, we completely determine the slopes and weights of the L-functions of an important class of exponential sums arising from analytic number theory. Our main tools include Adolphson-Sperber's work on toric exponential sums and…

By $p$-adically interpolating the branching law for the spherical pair $\left(U_n, U_{n+1} \times U_{n}\right)$ of definite unitary groups, we construct a $p$-adic $L$-function attached to cohomological automorphic representations of…