Related papers: Critical slope p-adic L-functions of CM modular fo…

The primary objective of this paper is the study of different instances of the elliptic Stark conjectures of Darmon, Lauder and Rotger, in a situation where the elliptic curve attached to the modular form $f$ has split multiplicative…

We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse H\"older constants associated to the weight. The method of proof uses a decoupling of the…

We present an elliptic curve analog of the Stark conjecture for the value of the $L$-function at $s=0$. Although implied by the general Beilinson conjectures, the approach here is very concrete. Several cases are proved.

If E is an elliptic curve over Q and K is an imaginary quadratic field, there is an Iwasawa main conjecture predicting the behavior of the Selmer group of E over the anticyclotomic Z_p-extension of K. The main conjecture takes different…

Let $K/F$ be a CM extension satisfying the ordinary assumption for an odd prime $p$ and let $\psi$ be a finite order anticyclotomic Hecke character of $K$. When $K$ has a place above $p$ of degree one, we apply Urban's method and the…

We apply the method of multiple Dirichlet series to develop $L$-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of quartic Hecke $L$-functions of prime moduli over the…

In this paper, we study quadratic forms in spaces of holomorphic cusp forms. We show, conditionally, that when two quadratic forms in Hecke eigenforms share no common diagonal terms, their inner product is expected to converge to the sum of…

In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one…

We prove an equivariant version of Beilinson's conjecture on non-critical $L$-values of strongly modular abelian varieties over number fields. As an application, we prove a weak version of Zagier's conjecture on $L(E,2)$ and Deninger's…

In this paper, we define the p-adic Euler L-functions using the fermionic p-adic integral on Zp. By computing the values of the p-adic Euler L-functions at negative integers, we show that for Dirichlet characters with odd conductor, this…

We unconditionally construct cyclotomic p-adic L-functions for Rankin-Selberg convolutions for GL(n+1) x GL(n) over arbitrary number fields, and show that they satisfy an expected functional equation.

Let f be a modular form of weight 2 and trivial character. Fix also an imaginary quadratic field K. We use work of Bertolini-Darmon and Vatsal to study the mu-invariant of the p-adic Selmer group of f over the anticyclotomic Zp-extension of…

In a recent paper, Castella and Hsieh proved results for Selmer groups associated with Galois representations attached to newforms twisted by Hecke characters of an imaginary quadratic field. These results are obtained under the so-called…

We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of H\"older regularity $C^{1/2}$, valued in $C^0_{t, loc} L^2_x$ endowed with the strong topology. The…

In this paper we give a proof of Deligne's conjecture on the critical values of $L$-functions for arbitrary algebraic Hecke characters. This extends a result of Blasius, which only works in the case of CM fields. The key new insight is that…

In order to considering the integrality of nearly holomorphic (vector-valued) Siegel modular forms, we introduce nearly Siegel modular forms and study their integrality. We show that the integrality of nearly Siegel modular forms in terms…

We establish the two-dimensional asymptotic distributions of the logarithm and logarithmic derivative of $L$-functions associated with a family of cubic Hecke characters. A crucial ingredient in the proof of our main result is an…

Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga-Sato variety over a suitable Shimura curve which gives rise…

In this work we prove congruences between special values of elliptic curves with CM that seem to play a central role in the analytic side of the non-commutative Iwasawa theory. These congruences are the analogue for elliptic curves with CM…

The purpose of this article is to establish theories concerning $p$-adic analogues of Hodge cohomology and Deligne-Beilinson cohomology with coefficients in variations of mixed Hodge structures. We first study log overconvergent…