Skip to main content

Joint Universality

  • Chapter
  • 1091 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1877)

In this chapter, we shall prove a conditional joint universality theorem for functions in S. Joint universality means that we are concerned with simultaneous uniform approximation, a topic invented by Voronin [362, 364]. Of course, such a result cannot hold for an arbitrary family of L-functions: e.g., ζ(s) and ζ(s)2 cannot be jointly universal. The L-functions need to be sufficiently independent to possess this joint universality property. We formulate sufficient conditions for a family of L-functions in order to be jointly universal and give examples when these conditions are fulfilled; for instance, Dirichlet L-functions to pairwise non-equivalent characters (this is an old result of Voronin) or twists of L-functions in the Selberg class subject to some condition on uniform distribution.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   59.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   79.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2007). Joint Universality. In: Value-Distribution of L-Functions. Lecture Notes in Mathematics, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44822-8_12

Download citation