scholarly journals Gross–Stark units and p-adic iterated integrals attached to modular forms of weight one

2016 ◽  
Vol 40 (2) ◽  
pp. 325-354 ◽  
Author(s):  
Henri Darmon ◽  
Alan Lauder ◽  
Victor Rotger
Keyword(s):  
Modular Forms ◽  
Iterated Integrals ◽  
Weight One ◽  
Stark Units

scholarly journals Beilinson–Flach elements, Stark units and 𝑝-adic iterated integrals

2019 ◽  
Vol 31 (6) ◽  
pp. 1517-1531
Author(s):  
Óscar Rivero ◽  
Victor Rotger
Keyword(s):  
Number Fields ◽  
Euler System ◽  
Iterated Integrals ◽  
Special Values ◽  
Weight One ◽  
Stark Units

AbstractWe study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in suitable number fields to special values of the Hida–Rankin p-adic L-function. We show that the latter conjecture follows from expected properties of Beilinson–Flach elements and prove the analogue of the main theorem of Castella and Hsieh about generalized Kato classes.

scholarly journals Three-loop contributions to the ρ parameter and iterated integrals of modular forms

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Samuel Abreu ◽  
Matteo Becchetti ◽  
Claude Duhr ◽  
Robin Marzucca
Keyword(s):  
Modular Forms ◽  
Iterated Integrals

scholarly journals Galois families of modular forms and application to weight one

2021 ◽  
Author(s):  
Sara Arias-de-Reyna ◽  
François Legrand ◽  
Gabor Wiese
Keyword(s):  
Modular Forms ◽  
Weight One

scholarly journals Feynman integrals and iterated integrals of modular forms

2018 ◽  
Vol 12 (2) ◽  
pp. 193-251 ◽  
Author(s):  
Luise Adams ◽  
Stefan Weinzierl
Keyword(s):  
Modular Forms ◽  
Iterated Integrals ◽  
Feynman Integrals

scholarly journals The modular equation and modular forms of weight one

1985 ◽  
Vol 100 ◽  
pp. 145-162 ◽  
Author(s):  
Toyokazu Hiramatsu ◽  
Yoshio Mimura
Keyword(s):  
Modular Forms ◽  
Quadratic Field ◽  
Congruence Subgroup ◽  
Algebraic Integer ◽  
Complex Multiplication ◽  
Cusp Forms ◽  
Imaginary Quadratic Fields ◽  
Modular Equation ◽  
Class Invariants ◽  
Weight One

This is a continuation of the previous paper [8] concerning the relation between the arithmetic of imaginary quadratic fields and cusp forms of weight one on a certain congruence subgroup. Let K be an imaginary quadratic field, say K = with a prime number q ≡ − 1 mod 8, and let h be the class number of K. By the classical theory of complex multiplication, the Hubert class field L of K can be generated by any one of the class invariants over K, which is necessarily an algebraic integer, and a defining equation of which is denoted byΦ(x) = 0.

scholarly journals Drinfeld Modular Forms of Weight One

1997 ◽  
Vol 67 (2) ◽  
pp. 215-228 ◽  
Author(s):  
Gunther Cornelissen
Keyword(s):  
Modular Forms ◽  
Drinfeld Modular Forms ◽  
Weight One

On ArtinL-functions associated to Hilbert modular forms of weight one

1983 ◽  
Vol 74 (1) ◽  
pp. 1-42 ◽  
Author(s):  
J. D. Rogawski ◽  
J. B. Tunnell
Keyword(s):  
Modular Forms ◽  
Hilbert Modular Forms ◽  
Hilbert Modular ◽  
Weight One
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