Computing modular degrees using $L$-functions

نویسندگان

چکیده

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computing modular degrees using L-functions

We give an algorithm to compute the modular degree of an elliptic curve defined over Q. Our method is based on the computation of the special value at s = 2 of the symmetric square of the L-function attached to the elliptic curve. This method is quite efficient and easy to implement.

متن کامل

Modular Symbols and L-functions

As the rst non-overview lecture in this seminar, we will be setting up a lot of notation, getting comfortable working with modular symbols, and then hopefully discussing some of the major inputs which make the theory work. The rst half of the talk we will work through the example of the unique cusp form of weight two and level 11 on X0(11). In the second half, we will bring in the theoretical r...

متن کامل

Modular Abelian Varieties of Odd Modular Degrees

In this paper, we will study modular Abelian varieties with odd congruence numbers by examining the cuspidal subgroup of J0(N). We will show that the conductor of such Abelian varieties must be of a special type. For example, if N is the conductor of an absolutely simple modular Abelian variety with an odd congruence number, then N has at most two prime divisors, and if N is odd, then N = p or ...

متن کامل

Computing Special Values of Motivic L-Functions

We present an algorithm to compute values L(s) and derivatives L(s) of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Γ-factor is of the form A ∏d i=1 Γ( s+λj 2 ) with d arbitrary and complex λj , not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).

متن کامل

Computing degree-1 L-functions rigorously

We describe a new, rigorous algorithm for efficiently and simultaneously computing many values of the Riemann zeta function on the critical line by exploiting the fast Fourier transform (FFT). We apply this to locating non-trivial zeros of zeta to high precision which are in turn used as input to our own implementation of the Lagarias and Odlyzko analytic algorithm to compute π(x), the prime co...

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

ژورنال

عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux

سال: 2003

ISSN: 1246-7405

DOI: 10.5802/jtnb.420