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math.NT2021
On Berndt's summation formula
Alexander E. Patkowski
We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the Mntz formula and the Poisson summation formula. By utilizing known properties…
math.NT2021
A remark on Fine's arithmetic functions
Alexander E. Patkowski
In this note, we take another look at some arithmetic identities of N.J. Fine associated with divisor functions. We connect these functions with indefinite quadratic forms using a…