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On Artin's Conjecture for Odd 2-Dimensional Representations

✍ Scribed by Basmaji J.

Book ID
127403601
Year
1994
Tongue
English
Weight
628 KB
Category
Library

No coin nor oath required. For personal study only.

✦ Synopsis

The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols.It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.

πŸ“œ SIMILAR VOLUMES

On Artin's Conjecture for Odd 2-dimensio
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✍ Jacques Basmaji, Ian Kiming, Martin Kinzelbach, Xiangdong Wang, LoΓ―c Merel (auth πŸ“‚ Library πŸ“… 1994 πŸ› Springer 🌐 English βš– 1010 KB

The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the

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Let a be an integer { &1 and not a square. Let P a (x) be the number of primes up to x for which a is a primitive root. Goldfeld and Stephens proved that the average value of P a (x) is about a constant multiple of xΓ‚ln x. Carmichael extended the definition of primitive roots to that of primitive \*