Skip to main content

Consequences of Universality

  • Chapter
  • 1107 Accesses

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

The phenomenon of universality has many interesting consequences. There are the classic results due to Bohr, mentioned in the introduction, as well as extensions of Ostrowski's theorem on the non-existence of algebraic di.erential equations for Dirichlet series (which actually was part of the 18th Hilbert problem). In this chapter, we prove generalizations for universal L-functions, we discuss a disproof of a conjecture on certain mean-square estimates due to Ramachandra by Andersson [1], and, finally, we study the value-distribution of linear combinations of shifts of universal Dirichlet series.

Keywords

  • Dirichlet Series
  • Critical Line
  • Critical Strip
  • Universality Theorem
  • Selberg Class

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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). Consequences of 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_10

Download citation