Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Weighted averages of modular $L$-values
HTML articles powered by AMS MathViewer

by Andrew Knightly and Charles Li PDF
Trans. Amer. Math. Soc. 362 (2010), 1423-1443 Request permission


Using an explicit relative trace formula on $\operatorname {GL}(2)$, we derive a formula for averages of modular $L$-values in the critical strip, weighting by Fourier coefficients, Hecke eigenvalues, and Petersson norms. As an application we show that a GRH holds for these averages as the weight or the level goes to $\infty$. We also use the formula to give explicit zero-free regions of the form $|\operatorname {Im}(s)|\le \tau _0$ for some particular modular $L$-functions.
Similar Articles
Additional Information
  • Andrew Knightly
  • Affiliation: Department of Mathematics and Statistics, Neville Hall, University of Maine, Orono, Maine 04469-5752
  • Charles Li
  • Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
  • Received by editor(s): January 31, 2008
  • Published electronically: September 25, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 1423-1443
  • MSC (2000): Primary 11F11, 11F30, 11F67, 11F70
  • DOI:
  • MathSciNet review: 2563735