Details

Subject(s)

• L-functions [Browse]

Author

• Fouvry, É. (Étienne) [Browse]
• Kowalski, Emmanuel, 1969- [Browse]
• Michel, Philippe [Browse]
• Milićević, Djordje, 1978- [Browse]
• Sawin, Will, 1993- [Browse]

Series

• Memoirs of the American Mathematical Society ; no. 1394. [More in this series]
• Memoirs of the American Mathematical Society, 0065-9266 ; number 1394 [More in this series]

Summary note

"For a fairly general family of L-functions, we survey the known consequences of the existence of asymptomatic formulas with power-saving error term for the (twisted) first and second moments of the central values in the family. We then consider in detail the important special case of teh family of twists of a fixed cusp form by primitive Dirichlet characters modulo a prime q, and prove that it satisfies such formulas. We derive arithmetic consequences: a positive proportion of central values L(f [circled times] x, 1/2) are non-zero, and indeed bounded from below; there exist many characters x for which the central L-value is very large; the probability of a large analytic rank decays exponentially fast. We finally show how the second moment estimate establishes a special case of a conjecture of Mazur and Rubin concerning the distribution of molecular symbols."--Page v.

Notes

Number 1394 (third of 6 numbers)

Bibliographic references

Includes bibliographical references (pages 145-148) and notation index.

Contents

• Chapter 1. The second moment theory of families of L-functions
• Chapter 2. Preliminaries
• Chapter 3. Algebraic exponential sums
• Chapter 4. Computation of the first twisted moment
• Chapter 5. Computation of the second twisted moment
• Chapter 6. Non-vanishing at the central point
• Chapter 7. Extreme values of twisted L-functions
• Chapter 8. Upper bounds for the analytic rank
• Chapter 9. A conjecture of Mazur-Rubin concerning modular symbols
• Notation index
• Bibliography.

Show 8 more Contents items

ISBN

• 9781470456788 ((paperback))
• 1470456788 ((paperback))

OCLC

1372138950

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