On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis
By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and p...
Збережено в:
| Дата: | 2012 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164138 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis / S.K. Sekatskii, S. Beltraminelli, D. Merlini // Український математичний журнал. — 2012. — Т. 64, № 2. — С. 218-228. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-164138 |
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dspace |
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irk-123456789-1641382020-02-23T18:29:00Z On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis Sekatskii, S.K. Beltraminelli, S. Merlini, D. Статті By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and present some of them as an example. It is shown that all earlier known equalities of this type, viz., the Wang equality, Volchkov equality, Balazard–Saias–Yor equality, and an equality established by one of the authors, are certain special cases of our general approach. Показано як за допомогою узагальненої теореми Лiттлвуда про контурний iнтеграл, що мiстить логарифм аналiтичної функцiї, можна отримати нескiнченну кiлькiсть iнтегральних рiвностей, що мiстять iнтеграли вiд логарифма ζ-функцiї Рiмана i є еквiвалентними гiпотезi Рiмана, i наведено кiлька таких рiвностей у якостi прикладу. Показано, що деякi вiдомi рiвностi такого типу, а саме, рiвностi Ванга, Волчкова, Балазарда – Сайаса – Йора та рiвнiсть, що встановлена одним iз авторiв, є частинними випадками нaшого загального пiдходу 2012 Article On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis / S.K. Sekatskii, S. Beltraminelli, D. Merlini // Український математичний журнал. — 2012. — Т. 64, № 2. — С. 218-228. — Бібліогр.: 10 назв. — англ. 1027-3190 http://dspace.nbuv.gov.ua/handle/123456789/164138 517 en Український математичний журнал Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Статті Статті |
| spellingShingle |
Статті Статті Sekatskii, S.K. Beltraminelli, S. Merlini, D. On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis Український математичний журнал |
| description |
By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and present some of them as an example. It is shown that all earlier known equalities of this type, viz., the Wang equality, Volchkov equality, Balazard–Saias–Yor equality, and an equality established by one of the authors, are certain special cases of our general approach. |
| format |
Article |
| author |
Sekatskii, S.K. Beltraminelli, S. Merlini, D. |
| author_facet |
Sekatskii, S.K. Beltraminelli, S. Merlini, D. |
| author_sort |
Sekatskii, S.K. |
| title |
On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis |
| title_short |
On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis |
| title_full |
On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis |
| title_fullStr |
On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis |
| title_full_unstemmed |
On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis |
| title_sort |
on equalities involving integrals of the logarithm of the riemann ζ-function and equivalent to the riemann hypothesis |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| topic_facet |
Статті |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/164138 |
| citation_txt |
On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis / S.K. Sekatskii, S. Beltraminelli, D. Merlini // Український математичний журнал. — 2012. — Т. 64, № 2. — С. 218-228. — Бібліогр.: 10 назв. — англ. |
| series |
Український математичний журнал |
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2023-10-18T22:12:53Z |
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