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.
ISBN
9781470456788 ((paperback))
1470456788 ((paperback))
OCLC
1372138950
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
Read more...