Skip to main content
×
Home
    • Aa
    • Aa

Small zeros of quadratic L-functions

  • Ali E. Özlük (a1) and C. Snyder (a1)
Abstract

We study the distribution of the imaginary parts of zeros near the real axis of quadratic L-functions. More precisely, let K(s) be chosen so that |K(1/2 ± it)| is rapidly decreasing as t increases. We investigate the asymptotic behaviour of

as D → ∞. Here denotes the sum over the non-trivial zeros p = 1/2 + of the Dirichlet L-function L(s, χd), and χd = () is the Kronecker symbol. The outer sum is over all fundamental discriminants d that are in absolute value ≤ D. Assuming the Generalized Riemann Hypothesis, we show that for

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Small zeros of quadratic L-functions
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Small zeros of quadratic L-functions
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Small zeros of quadratic L-functions
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[3]H.-J. Bentz and J. Pintz , ‘Quadratic residues and the distribution of prime numbers’, Monatshefte für Mathematik 90 (1982), 91100.

[4]H.-J. Bentz , ‘Discrepancies in the distribution of prime numbers’, J. Number Theory 15 (1982), 252274.

[6]H. Davenport , Multiplicative number theory, 2nd ed. (Springer-Verlag, Berlin, Heidelberg, New York, 1980).

[9]D. Shanks , ‘Quadratic residues and the distribution of primes’, Math. Tables and other Aids to Comp. 13 (1959), 272284.

[11]P.J. Weinberger , ‘On small zeros of Dirichlet L-functions’, Math. Comp. 29 (1975), 319328.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax