scholarly journals On modular forms for some noncongruence subgroups of SL2 (ℤ) II

2009 ◽  
Vol 41 (4) ◽  
pp. 589-598 ◽  
Author(s):  
Chris Kurth ◽  
Ling Long
Keyword(s):  
Modular Forms ◽  
Noncongruence Subgroups

scholarly journals Modular Forms on Noncongruence Subgroups and Atkin–Swinnerton-Dyer Relations

2010 ◽  
Vol 19 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Liqun Fang ◽  
J. William Hoffman ◽  
Benjamin Linowitz ◽  
Andrew Rupinski ◽  
Helena Verrill
Keyword(s):  
Modular Forms ◽  
Noncongruence Subgroups

scholarly journals Modular Forms For Noncongruence Subgroups

2005 ◽  
Vol 1 (1) ◽  
pp. 205-221 ◽  
Author(s):  
Wen-Ching Winnie Li ◽  
Ling Long ◽  
Zifeng Yang
Keyword(s):  
Modular Forms ◽  
Noncongruence Subgroups

scholarly journals On modular forms for some noncongruence subgroups of SL2(Z)

2008 ◽  
Vol 128 (7) ◽  
pp. 1989-2009 ◽  
Author(s):  
Chris A. Kurth ◽  
Ling Long
Keyword(s):  
Modular Forms ◽  
Noncongruence Subgroups

scholarly journals Iwasawa Theory of Elliptic Modular Forms Over Imaginary Quadratic Fields at Non-ordinary Primes

2019 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Euler System ◽  
Base Change ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Selmer Groups ◽  
Imaginary Quadratic Fields ◽  
Elliptic Modular Form

AbstractThis article is a continuation of our previous work [7] on the Iwasawa theory of an elliptic modular form over an imaginary quadratic field $K$, where the modular form in question was assumed to be ordinary at a fixed odd prime $p$. We formulate integral Iwasawa main conjectures at non-ordinary primes $p$ for suitable twists of the base change of a newform $f$ to an imaginary quadratic field $K$ where $p$ splits, over the cyclotomic ${\mathbb{Z}}_p$-extension, the anticyclotomic ${\mathbb{Z}}_p$-extensions (in both the definite and the indefinite cases) as well as the ${\mathbb{Z}}_p^2$-extension of $K$. In order to do so, we define Kobayashi–Sprung-style signed Coleman maps, which we use to introduce doubly signed Selmer groups. In the same spirit, we construct signed (integral) Beilinson–Flach elements (out of the collection of unbounded Beilinson–Flach elements of Loeffler–Zerbes), which we use to define doubly signed $p$-adic $L$-functions. The main conjecture then relates these two sets of objects. Furthermore, we show that the integral Beilinson–Flach elements form a locally restricted Euler system, which in turn allow us to deduce (under certain technical assumptions) one inclusion in each one of the four main conjectures we formulate here (which may be turned into equalities in favorable circumstances).

scholarly journals Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms

2018 ◽  
Vol 30 (4) ◽  
pp. 887-913 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Main Conjecture ◽  
Elliptic Modular Form

Abstract This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic {\mathbb{Z}_{p}} -tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson–Flach elements.

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