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Ray class field extensions of real quadratic fields and solvability of congruences

โœ Scribed by Paul B. Massell

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
553 KB
Volume
20
Category
Article
ISSN
0022-314X

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๐Ÿ“œ SIMILAR VOLUMES

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We show that for a real quadratic field F the dihedral congruence primes with respect to F for cusp forms of weight k and quadratic nebentypus are essentially the primes dividing expressions of the form e kร€1 รพ AE 1 where e รพ is a totally positive fundamental unit of F . This extends work of Hida.

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Let F be a quadratic field and p a prime ideal in F. Then we ask whether the ray class field of F mod p has a normal integral basis over F. We see many differences between our case and the case where the base field F is the field of rational numbers.