p-ADIC CLASS INVARIANTS

نویسندگان

  • Reinier Bröker
  • REINIER BRÖKER
چکیده

We develop a new p-adic algorithm to compute the minimal polynomial of a class invariant. Our approach works for virtually any modular function yielding class invariants. The main algorithmic tool is modular polynomials, a concept which we generalize to functions of higher level.

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

GALOIS MODULES AND p-ADIC REPRESENTATIONS

In this paper we develop a theory of class invariants associated to p-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to p-adic representations in terms of resolvends associated to torsors of finite group schemes.

متن کامل

Hilbert modular forms and the Gross-Stark conjecture

Let F be a totally real field and χ an abelian totally odd character of F . In 1988, Gross stated a p-adic analogue of Stark’s conjecture that relates the value of the derivative of the p-adic L-function associated to χ and the p-adic logarithm of a p-unit in the extension of F cut out by χ. In this paper we prove Gross’s conjecture when F is a real quadratic field and χ is a narrow ring class ...

متن کامل

ON p-ADIC PROPERTIES OF TWISTED TRACES OF SINGULAR MODULI

We prove that logarithmic derivatives of certain twisted Hilbert class polynomials are holomorphic modular forms modulo p of filtration p+1. We derive p-adic information about twisted Hecke traces and Hilbert class polynomials. In this framework we formulate a precise criterion for p-divisibility of class numbers of imaginary quadratic fields in terms of the existence of certain cusp forms modu...

متن کامل

CLASS INVARIANTS AND p-ADIC HEIGHTS

Let F be a number field with ring of integers OF , and let E/OF be an abelian scheme of arbitrary dimension. In this paper, we study the class invariant homomoprhisms on E with respect to powers of a prime p of ordinary reduction of E. Our main result implies that if the p-adic Birch and Swinnerton-Dyer conjecture holds for E, then the kernels of these homomorphisms are of bounded order. It fol...

متن کامل

MODELLING λ - INVARIANTS BY p - ADIC RANDOM MATRICES

How often is the p-adic λ-invariant of an imaginary quadratic field equal to m? We model this by the statistics of random p-adic matrices, and test these predictions numerically.

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