The second moment theory of families of L-functions : the case of twisted Hecke L-functions / Valentin Blomer, Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, Djordje Milićević, Will Sawin. - Princeton University Library Catalog

The second moment theory of families of L-functions : the case of twisted Hecke L-functions / Valentin Blomer, Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, Djordje Milićević, Will Sawin.

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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