On the  L ‐functions of the curves  y  2  =  x  ℓ  +  A | Zendy

Masri Riad | Zendy

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On the L ‐functions of the curves y 2 = x ℓ + A

Author(s) -

Masri Riad

Publication year - 2008

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/jdn040

Subject(s) - mathematics , eisenstein series , integer (computer science) , function field , prime (order theory) , combinatorics , series (stratigraphy) , algebraic number field , field (mathematics) , pure mathematics , modular form , paleontology , computer science , biology , programming language

Let ℓ > 3 be an odd prime and let A be an integer not divisible by ℓ. Let C A be the non‐singular projective model over ℚ of the affine curve C A : y 2 = x ℓ + A . In this paper, we use the theory of Hilbert modular Eisenstein series to obtain a formula for the central value of the Hasse–Weil L ‐function L ( C A , s ) of the curve C A when the cyclotomic field ℚ(ζ ℓ ) has ideal class number 1.

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