Bounding the Elliptic Mahler Measure Ii

نویسندگان

  • Graham Everest
  • Chris Pinner
چکیده

The theory of heights for rational points on arithmetic elliptic curves is becoming well known. An important fact in the basic theory is the relationship between the na ve and the canonical height of a rational point; in fact they diier by a uniformly bounded amount. In this note, we provide a generalisation of this fact from the point of view of heights of polynomials, rather than heights of points. We extend this concept to polynomials in several variables.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

From L-series of Elliptic Curves to Mahler Measures

We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L-values of CM elliptic curves of conductors 27 and 36. Furthermore, we prove a new functional equation for the Mahler measure of the polynomial family (1 +X)(1 + Y )(X + Y )− αXY , α ∈ R.

متن کامل

The Mahler Measure for Arbitrary Tori

We consider a variation of the Mahler measure where the defining integral is performed over a more general torus. We focus our investigation on two particular polynomials related to certain elliptic curve E and we establish new formulas for this variation of the Mahler measure in terms of L′(E, 0).

متن کامل

On the Mahler Measure Of

We prove a conjectured formula relating the Mahler measure of the Laurent polynomial 1 + X + X−1 + Y + Y −1, to the L-series of a conductor 15 elliptic curve.

متن کامل

On the Mahler Measure of 1 + X +

We prove a conjectured formula relating the Mahler measure of the Laurent polynomial 1 + X + X−1 + Y + Y −1 to the L-series of a conductor 15 elliptic curve.

متن کامل

A Dynamical Interpretation of the Global Canonical Height on an Elliptic Curve

There is a well–understood connection between polynomials and certain simple algebraic dynamical systems. In this connection, the Mahler measure corresponds to the topological entropy, Kronecker’s Theorem relates ergodicity to positivity of entropy, approximants to the Mahler measure are related to growth rates of periodic points, and Lehmer’s problem is related to the existence of algebraic mo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007