The Second Moment Theory of Families of 𝐿-Functions–The Case of Twisted Hecke 𝐿-Functions
Page 1 Number 1394 The Second Moment Theory of Families of L-Functions–The Case of …

Abstract Mazur, Rubin, and Stein have recently formulated a series of conjectures about
statistical properties of modular symbols in order to understand central values of twists of …

For a fairly general family of L-functions, we survey the known consequences of the
existence of asymptotic formulas with power-sawing error term for the (twisted) first and …

The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn
Stevens, gives a beautiful and effective construction of the p‐adic L‐function of a modular …

Let K be an imaginary quadratic field with class number 1, in this paper we obtain the
functional equation of the p-adic L-function of small slope p-stabilised Bianchi modular …

Extending the former work for the good reduction case, we provide a numerical criterion to
verify a large portion of the “Iwasawa main conjecture without p-adic L-functions” for elliptic …

We prove that the central values of additive twists of a cuspidal L-function define a quantum
modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau …

We prove a version of the conjecture of Fukaya and Kato concerning the existence of p-adic
L-functions for motives in the case of certain Hida families of modular forms and for …

Let $ X $ be a quotient of the modular curve $ X_0 (N) $ whose Jacobian $ J_X $ is a simple
factor of $ J_0 (N)^{new} $ over $\mathbf {Q} $. Let $ f $ be the newform of level $ N $ and …

We reinterpret the explicit construction of Gross points given by Chida-Hsieh as a non-
Archimedian analogue of the standard geodesic cycle (i∞)-(0) on the Poincaré upper half …