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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">cheb</journal-id><journal-title-group><journal-title xml:lang="ru">Чебышевский сборник</journal-title><trans-title-group xml:lang="en"><trans-title>Chebyshevskii Sbornik</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-8383</issn><publisher><publisher-name>Tula State Lev Tolstoy  Pedagogical University</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">cheb-379</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Article</subject></subj-group></article-categories><title-group><article-title>ПРЕОБРАЗОВАНИЕ ЛАПЛАСА ДЛЯ L-ФУНКЦИЙ ДИРИХЛЕ</article-title><trans-title-group xml:lang="en"><trans-title>THE LAPLACE TRANSFORM OF DIRICHLET L-FUNCTIONS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бальчюнас</surname><given-names>А.</given-names></name><name name-style="western" xml:lang="en"><surname>Balˇciu¯nas</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Вильнюс.</p></bio><bio xml:lang="en"><p>Vilnius.</p></bio></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мацайтене</surname><given-names>Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Macaitiene˙</surname><given-names>R.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шяуляй</p></bio><bio xml:lang="en"><p>ˇSiauliai.</p></bio></contrib></contrib-group><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>08</day><month>03</month><year>2018</year></pub-date><volume>18</volume><issue>4</issue><fpage>86</fpage><lpage>96</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Бальчюнас А., Мацайтене Р., 2018</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="ru">Бальчюнас А., Мацайтене Р.</copyright-holder><copyright-holder xml:lang="en">Balˇciu¯nas A., Macaitiene˙ R.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.chebsbornik.ru/jour/article/view/379">https://www.chebsbornik.ru/jour/article/view/379</self-uri><abstract><p>.</p></abstract><trans-abstract xml:lang="en"><p>.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>L-функция Дирихле</kwd><kwd>преобразование Лапласа</kwd><kwd>преобразование Меллина</kwd><kwd>дзета-функция Римана</kwd></kwd-group><kwd-group xml:lang="en"><kwd>L-function</kwd><kwd>Laplace transform</kwd><kwd>Mellin transform</kwd><kwd>Riemann zetafunction</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Atkinson A.A., The mean value of the zeta-function on the critical line // Quart. 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