相关论文: Central derivatives of L-functions in Hida familie…

The theme of this work is the study of the Nekov\'a\v{r}-Selmer group H^1_f(K,T) attached to a twisted Hida family T of Galois representations and a quadratic number field K. The results that we obtain have the following shape: if a twisted…

We study the vanishing of $L(f,\chi,j)$ as $f$ runs through all classical forms in a $p$-adic Hida family (including forms with arbitrarily high nebentype at $p$), $\chi$ runs through all characters of $p$-power conductor, and $j$ is a…

We prove under mild hypotheses the three-variable Iwasawa main conjecture for $p$-ordinary modular forms in the indefinite setting. Our result is in a setting complementary to that in the work of Skinner-Urban, and it has applications to…

Let r : G_Q -> GL_2(Fpbar) be a p-ordinary and p-distinguished irreducible residual modular Galois representation. We show that the vanishing of the algebraic or analytic Iwasawa mu-invariant of a single modular form lifting r implies the…

We build a one-variable $p$-adic $L$-function attached to two Hida families of ordinary $p$-stabilised newforms $\mathbf{f}$, $\mathbf{g}$, interpolating the algebraic part of the central values of the complex $L$-series $L(f \otimes…

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…

We provide a simple and efficient numerical criterion to verify the Iwasawa main conjecture and the indivisibility of derived Kato's Euler systems for modular forms of weight two at any good prime under mild assumptions. In the ordinary…

In this paper we construct a two variables $p$-adic $L$-function for the standard representation associated with a Hida family of parallel weight genus $g$ Siegel forms, using a method previously developed by B\"ocherer--Schmidt in one…

A quadratic twist of the L-function associated with a modular form is known to satisfy a functional equation, which may be even or odd. A result due to Gross and Zagier explicitly computes the central value of the L-function or its…

For a newform for Gamma_0(N) of even weight k, we prove that its attached p-adic L-function is not identically zero on the group Z_p of the p-adic units. If p >3, we prove that the order of vanishing at any p-adic integer is finite.

We show a non-vanishing result for the averages of the derivatives of $L$-functions associated with the orthogonal basis of the space of vector-valued cusp forms of weight $k\in \frac12 \mathbb{Z}$ on the full group in the critical strip.…

Bertolini-Darmon and Mok proved a formula of the second derivative of the two-variable $p$-adic $L$-function of a modular elliptic curve over a totally real field along the Hida family in terms of the image of a global point by some…

Using the $\scr L$-invariant constructed in our previous paper we prove a Mazur-Tate-Teitelbaum style formula for derivatives of p-adic L-functions of elliptic modular forms at near central points. In the second version of the paper the…

The aim of this paper is to prove inequalities towards instances of the Bloch-Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the $L$-function at the central point is zero or one. We achieve…

The purpose of this paper is to build on results in {\it{higher codimension Iwasawa theory}}. The setting of our results involves Galois representations arising as cyclotomic twist deformations associated to (i) the tensor product of two…

In this paper, we show that, on average, the derivatives of $L$-functions of cuspidal Hilbert modular forms with sufficiently large weight $k$ do not vanish on the line segments $\Im(s)=t_{0}$,…

The aim of this note is to compare several anticyclotomic $p$-adic $L$-functions for modular forms and $p$-adic families of ordinary modular forms, which have been defined and studied from different perspectives by Skinner-Urban, Hida,…

The point of this paper is to give an explicit p-adic analytic construction of two Iwasawa functions L_p^\sharp(f,T) and L_p^\flat(f,T) for a weight two modular form \sum a_n q^n and a good prime p. This generalizes work of Pollack who…

We develop a new strategy for studying low weight specializations of $p$-adic families of ordinary modular forms. In the elliptic case, we give a new proof of a result of Ghate--Vatsal which states that a Hida family contains infinitely…

Let $F$ be a totally real field and let $E/F$ be a CM quadratic extension. We construct a $p$-adic $L$-function attached to Hida families for the group ${\rm GL}_{2/F}\times {\rm Res}_{E/F}{\rm GL}_{1}$. It is characterised by an exact…