相关论文: Multivariate p-dic L-function

We extend the construction of the $p$-adic $L$-function interpolating unitary Friedberg--Jacquet periods in previous work of the author to include the $p$-adic variation of Maass--Shimura differential operators. In particular, we develop a…

By using q-Volkenborn integral on Z_{p}, we (simsek, simsekCanada) constructed new generating functions of the (h,q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to the generating functions, we constructed…

Let $A$ be an abelian variety over the function field of a smooth projective curve $C$ over an algebraically closed field $k$. We compute the $l$-adic cohomology groups of $C$ with coefficients in the locally constant sheaf associated to…

We prove p-adic functoriality for inner forms of unitary groups in three variables by establishing the existence of morphisms between eigenvarieties that extend the classical Langlands functoriality.

We propose a new method to apply the Lipschitz functional calculus of local Dirichlet forms to Poisson random measures.

In the previous paper we generalized Greenberg's construction of the $\Cal L$-invariant to semistable representations. Here we prove that this construction is compatible with Perrin-Riou's theory of $p$-adic $L$-functions

We study several types of multivalued functions in digital topology.

For ordinary modular forms, there are two constructions of a p-adic L-function attached to the non-unit root of the Hecke polynomial, which are conjectured but not known to coincide. We prove this conjecture for modular forms of CM type, by…

We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.

We continue our investigations of the analytic properties of nonlinear twists of L-functions developed in [4],[5] and [7]. Given an L-function of degree d, we first extend the transformation formula in [5], relating a twist with leading…

We prove a version of L'hospital's rule for multivariable functions, which holds for non-isolated singular points. We also give an algorithm for resolving many indeterminate limits with isolated singular points.

We compute the Archimedean doubling zeta integrals which appear in the interpolation formulas for the p-adic L-functions of Siegel modular forms, and verify that they agree with the modified Archimedean Euler factors for p-adic…

We construct the four-variable primitive $p$-adic $L$-functions associated with the triple product of Hida families and prove the explicit interpolation formulae at all critical values in the balanced range. Our construction is to carry out…

We discuss modular forms as objects of computer algebra and as elements of certain p-adic Banach modules. Problem-solving approach in number theory is discussed which is based on the use of generating functions and their links with modular…

We study analytic properties of multiple zeta-functions of generalized Hurwitz-Lerch type. First, as a special type of them, we consider multiple zeta-functions of generalized Euler-Zagier-Lerch type and investigate their analytic…

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,…

Let p be an odd prime and F a totally real number field. Let f be a Hilbert cuspidal eigenform of parallel weight 2, trivial Nebentypus and ordinary at p. It is possible to construct a p-adic L-function which interpolates the complex…

For every triple F,K,p where F is a classical elliptic eigenform, K is a quadratic imaginary field and p> 3 is a prime integer which is not split in K, we attach a p-adic L function which interpolates the algebraic parts of the special…

We study the Iwasawa $\lambda$-invariant of Dirichlet characters $\chi$ of arbitrary order for odd primes $p$. From special values of the $p$-adic $L$-function and its derivative we derive several novel and easily computable criteria to…

In this article, we present a new linear independence criterion for values of the $p$-adic polygamma functions defined by J.~Diamond. As an application, we obtain the linear independence of some families of values of the $p$-adic Hurwitz…