Double Series of Bessel Functions and the Circle and Divisor Problems

George E. Andrews and Bruce C. Berndt
Additional contact information
George E. Andrews: The Pennsylvania State University, Department of Mathematics
Bruce C. Berndt: University of Illinois at Urbana-Champaign, Department of Mathematics

Chapter 2 in Ramanujan's Lost Notebook, 2013, pp 7-91 from Springer

Abstract: Abstract This chapter is devoted to proofs of two remarkable identities involving infinite series of Bessel functions. One identity is associated with the classical circle problem, while the other is connected with the equally difficult divisor problem. Each of the identities is open to three different interpretations, with entirely different proofs needed for each interpretation. New methods of estimating trigonometric sums are introduced in our proofs.

Keywords: Bessel Function; Uniform Convergence; Dirichlet Series; Double Series; Dyadic Interval (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-4081-9_2

Ordering information: This item can be ordered from
http://www.springer.com/9781461440819

DOI: 10.1007/978-1-4614-4081-9_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().