scholarly journals PARAMETRIZING ELLIPTIC CURVES BY MODULAR UNITS

2015 ◽  
Vol 100 (1) ◽  
pp. 33-41 ◽  
Author(s):  
FRANÇOIS BRUNAULT
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Recent Work ◽  
Short Note ◽  
Torsion Subgroup ◽  
Modular Functions ◽  
Open Questions ◽  
Modular Units

It is well known that every elliptic curve over the rationals admits a parametrization by means of modular functions. In this short note, we show that only finitely many elliptic curves over $\mathbf{Q}$ can be parametrized by modular units. This answers a question raised by W. Zudilin in a recent work on Mahler measures. Further, we give the list of all elliptic curves $E$ of conductor up to 1000 parametrized by modular units supported in the rational torsion subgroup of $E$. Finally, we raise several open questions.

scholarly journals LOCAL HEIGHTS ON ELLIPTIC CURVES AND INTERSECTION MULTIPLICITIES

2012 ◽  
Vol 08 (06) ◽  
pp. 1477-1484
Author(s):  
VINCENZ BUSCH ◽  
JAN STEFFEN MÜLLER
Keyword(s):  
Elliptic Curves ◽  
Short Note ◽  
Number Fields ◽  
Intersection Theory ◽  
Ring Of Integers ◽  
Regular Model ◽  
Intersection Multiplicities

In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.

Threshold verifiable multi-secret sharing based on elliptic curves and Chinese remainder theorem

2019 ◽  
Vol 13 (3) ◽  
pp. 278-284 ◽  
Author(s):  
Maryam Sheikhi-Garjan ◽  
Mojtaba Bahramian ◽  
Christophe Doche
Keyword(s):  
Elliptic Curves ◽  
Secret Sharing ◽  
Chinese Remainder Theorem ◽  
Multi Secret Sharing

scholarly journals A short note on inadmissible coefficients of weight 2 and $$2k+1$$ newforms

2021 ◽  
Author(s):  
Malik Amir ◽  
Andreas Hatziiliou
Keyword(s):  
Elliptic Curves ◽  
Fourier Coefficients ◽  
Short Note ◽  
Galois Representation ◽  
Dirichlet Character ◽  
K3 Surfaces ◽  
Integer Coefficients

AbstractLet $$f(z)=q+\sum _{n\ge 2}a(n)q^n$$ f ( z ) = q + ∑ n ≥ 2 a ( n ) q n be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan J, 2021) for $$k=2$$ k = 2 by ruling out or locating all odd prime values $$|\ell |<100$$ | ℓ | < 100 of their Fourier coefficients a(n) when n satisfies some congruences. We also study the case of odd weights $$k\ge 1$$ k ≥ 1 newforms where the nebentypus is given by a quadratic Dirichlet character.

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

Introduction

2018 ◽  
Author(s):  
Peter Hopkins
Keyword(s):  
Final Section ◽  
Short Note ◽  
Current Situation ◽  
Research Projects ◽  
Everyday Lives ◽  
Early Settlement ◽  
The Everyday ◽  
Initial Research

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.

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