4 papers
On values of finite multiple harmonic -series at roots of unity
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
We mainly answer two open questions about finite multiple harmonic -series on 3-2-1 indices at roots of unity, posed recently by H. Bachmann, Y. Takeyama, and K. Tasaka. Two con…
Multiple zeta star values on 3-2-1 indices
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In 2008, Muneta found explicit evaluation of the multiple zeta star value , and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3-2-1 i…
Generating functions for multiple zeta star values
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler su…
Multiple harmonic sums and multiple harmonic star sums are (nearly) never integers
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
It is well known that the harmonic sum is never an integer for . In 1946, Erdős and Niven proved that the nested multiple harmonic sum $H_n(\{…