Explicit formulae for L-functions: Difference between revisions

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==References==

{{reflist|25em}}

*{{Citation | authorlinkauthor-link=Albert Ingham | last1=Ingham | first1=A.E. | title=The Distribution of Prime Numbers | publisher=[[Cambridge University Press]] | isbn=978-0-521-39789-6 | mr=1074573 | year=1990 | zbl=0715.11045 | edition=2nd | origyearorig-date=1932 | series=Cambridge Tracts in Mathematics and Mathematical Physics | volume=30 | others=reissued with a foreword by [[Robert Charles Vaughan (mathematician)|R. C. Vaughan]] }}

*{{citation | last=Lang | first=Serge | authorlinkauthor-link=Serge Lang | title=Algebraic number theory | edition=2nd | series=Graduate Texts in Mathematics | volume=110 | ___location=New York, NY | publisher=[[Springer-Verlag]] | year=1994 | isbn=0-387-94225-4 | zbl=0811.11001 }}

*{{Citation | last1=Riemann | first1=Bernhard | title=Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse | url=http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/ | year=1859 | journal=Monatsberichte der Berliner Akademie}}

*{{Citation | last1=Weil | first1=André | author1-link=André Weil | title=Sur les "formules explicites" de la théorie des nombres premiers | trans-title=On "explicit formulas" in the theory of prime numbers | mr=0053152 | year=1952 | journal=Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] | volume=Tome Supplémentaire | pages=252–265 | zbl=0049.03205 | language=fr }}

*{{Citation | last1 = von Mangoldt | first1 = Hans | title=Zu Riemanns Abhandlung "Über die Anzahl der Primzahlen unter einer gegebenen Grösse" | journal = [[Journal für die reine und angewandte Mathematik]] | volume=114 | year=1895 | pages=255–305 | jfm=26.0215.03 | language=de | issn=0075-4102 | mr=1580379 | trans-title=On Riemann's paper "The number of prime numbers less than a given magnitude" }}

*{{Citation | last1 = Meyer | first1 = Ralf | title=On a representation of the idele class group related to primes and zeros of ''L''-functions | journal = [[Duke Math. J.]] | volume=127 | number=3 | year=2005 | pages=519–595 | zbl=1079.11044 | issn=0012-7094 | doi=10.1215/s0012-7094-04-12734-4 | mr=2132868 | ref=harv| arxiv=math/0311468 }}

*{{citation | last = Zagier | first = Don | authorlink author-link= Don Zagier | doi = 10.1007/bf03351556 | issue = S2 | journal = [[The Mathematical Intelligencer]] | pages = 7–19 | title = The first 50 million prime numbers | volume = 1 | year = 1977}}

* Garcia J.J Mellin Convolution and its Extensions, Perron Formula and Explicit Formulae doi=10.20944/preprints201801.0020.v1

* https://encyclopediaofmath.org/wiki/M%C3%B6bius_function#:~:text=The%20M%C3%B6bius%20function%20is%20an,M%C3%B6bius%20in%201832

==Further reading==

* {{citation | last=Edwards | first=H.M. | authorlinkauthor-link=Harold Edwards (mathematician) | title=Riemann's zeta function | series=Pure and Applied Mathematics | volume=58 | ___location=New York-London |publisher=Academic Press | year=1974 | isbn=0-12-232750-0 | zbl=0315.10035 }}

* {{citation | last=Riesel | first=Hans | authorlinkauthor-link=Hans Riesel | title=Prime numbers and computer methods for factorization | edition=2nd | series=Progress in Mathematics | volume=126 | ___location=Boston, MA | publisher=Birkhäuser | year=1994 | isbn=0-8176-3743-5 | zbl=0821.11001 }}

[[Category:Zeta and L-functions]]