Dirichlet summations and products over primes
We derive new classes of infinite products taken over the primes, for example expressing ∏p(11−p−n)(1−p−m)−1 as an infinite produce of Riemann zeta functions, this product being taken over the set of rational numbers α/β geater than zero with a relatively prime to βζ(n)∏α,βζ(αm+βn)1/β....
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000444 |
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| _version_ | 1832550025489547264 |
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| author | Geoffrey B. Campbell |
| author_facet | Geoffrey B. Campbell |
| author_sort | Geoffrey B. Campbell |
| collection | DOAJ |
| description | We derive new classes of infinite products taken over the primes, for example
expressing
∏p(11−p−n)(1−p−m)−1
as an infinite produce of Riemann zeta functions, this product being taken over the set of rational
numbers α/β geater than zero with a relatively prime to βζ(n)∏α,βζ(αm+βn)1/β. |
| format | Article |
| id | doaj-art-abd7ead96a4647cb8fe1bc65e12474f0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-abd7ead96a4647cb8fe1bc65e12474f02025-02-03T06:07:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116235937210.1155/S0161171293000444Dirichlet summations and products over primesGeoffrey B. Campbell021 Wurruk Avenue, Preston, Victoria 3072, AustraliaWe derive new classes of infinite products taken over the primes, for example expressing ∏p(11−p−n)(1−p−m)−1 as an infinite produce of Riemann zeta functions, this product being taken over the set of rational numbers α/β geater than zero with a relatively prime to βζ(n)∏α,βζ(αm+βn)1/β.http://dx.doi.org/10.1155/S0161171293000444 |
| spellingShingle | Geoffrey B. Campbell Dirichlet summations and products over primes International Journal of Mathematics and Mathematical Sciences |
| title | Dirichlet summations and products over primes |
| title_full | Dirichlet summations and products over primes |
| title_fullStr | Dirichlet summations and products over primes |
| title_full_unstemmed | Dirichlet summations and products over primes |
| title_short | Dirichlet summations and products over primes |
| title_sort | dirichlet summations and products over primes |
| url | http://dx.doi.org/10.1155/S0161171293000444 |
| work_keys_str_mv | AT geoffreybcampbell dirichletsummationsandproductsoverprimes |