Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On a Conjecture of Bateman About r5(n)


Affiliations
1 Department of Mathematics and Statistics, Queen’s University, Kingston, Canada
     

   Subscribe/Renew Journal


Let r5(n) be the number of ways of writing n as a sum of five integer squares. In his study of this function, Bateman was led to formulate a conjecture regarding the sum Σ|j|≤√n σ(n−j2) where σ(n) is the sum of positive divisors of n. We give a proof of Bateman’s conjecture in the case n is square-free and congruent to 1 (mod 4).
User
Subscription Login to verify subscription
Notifications
Font Size


  • On a Conjecture of Bateman About r5(n)

Abstract Views: 306  |  PDF Views: 0

Authors

Arpita Kar
Department of Mathematics and Statistics, Queen’s University, Kingston, Canada
M. Ram Murty
Department of Mathematics and Statistics, Queen’s University, Kingston, Canada

Abstract


Let r5(n) be the number of ways of writing n as a sum of five integer squares. In his study of this function, Bateman was led to formulate a conjecture regarding the sum Σ|j|≤√n σ(n−j2) where σ(n) is the sum of positive divisors of n. We give a proof of Bateman’s conjecture in the case n is square-free and congruent to 1 (mod 4).

References