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July 7, 2009 15:24 WSPC/INSTRUCTION FILE vissqijnt Squareness in the special L-value and special L-values of twists
 

Summary: July 7, 2009 15:24 WSPC/INSTRUCTION FILE vissqijnt
Squareness in the special L-value and special L-values of twists
Amod Agashe
Department of Mathematics, Florida State University
Tallahassee, FL 32306, U.S.A.
agashe@math.fsu.edu
Received (Day Month Year)
Accepted (Day Month Year)
Communicated by xxx
Let N be a prime and let A be a quotient of J0(N) over Q associated to a newform
such that the special L-value of A (at s = 1) is non-zero. Suppose that the algebraic
part of the special L-value of A is divisible by an odd prime q such that q does not
divide the numerator of N-1
12
. Then the Birch and Swinnerton-Dyer conjecture predicts
that the q-adic valuations of the algebraic part of the special L-value of A and of the
order of the Shafarevich-Tate group are both positive even numbers. Under a certain
mod q non-vanishing hypothesis on special L-values of twists of A, we show that the
q-adic valuations of the algebraic part of the special L-value of A and of the Birch and
Swinnerton-Dyer conjectural order of the Shafarevich-Tate group of A are both positive

  

Source: Agashe, Amod - Department of Mathematics, Florida State University

 

Collections: Mathematics