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.

Blomer, Valentin [Browse]
  • Providence, RI : AMS, American Mathematical Society, 2023.
  • ©2023
v, 148 pages ; 26 cm


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.
Number 1394 (third of 6 numbers)
Bibliographic references
Includes bibliographical references (pages 145-148) and notation index.
  • 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.
  • 9781470456788 ((paperback))
  • 1470456788 ((paperback))
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