TY - JOUR
T1 - An integral of Dedekind An integral of Dedekind An integral of Dedekind An integral of Dedekind eta-functions in Ramanujans lost notebook
AU - Berndt, Bruce C.
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© Walter de Gruyter Berlin , New York 2002.
PY - 2002/9/30
Y1 - 2002/9/30
N2 - On page 207 in his lost notebook, Ramanujan recorded a curious formula for an integral of a certain quotient of Dedekind eta-functions. The formula involves a mysterious constant C, which Ramanujan claims, with two question marks appended, is a simple multiple of a Dirichlet L-function evaluated at the argument 2. The integral formula was first proved by S. H. Son, but he did not establish Ramanujan's formula for C. We give an entirely diÂerent proof of this result which also shows that Ramanujan's questioned formula for C is correct.
AB - On page 207 in his lost notebook, Ramanujan recorded a curious formula for an integral of a certain quotient of Dedekind eta-functions. The formula involves a mysterious constant C, which Ramanujan claims, with two question marks appended, is a simple multiple of a Dirichlet L-function evaluated at the argument 2. The integral formula was first proved by S. H. Son, but he did not establish Ramanujan's formula for C. We give an entirely diÂerent proof of this result which also shows that Ramanujan's questioned formula for C is correct.
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U2 - 10.1515/crll.2002.084
DO - 10.1515/crll.2002.084
M3 - Article
AN - SCOPUS:85085591726
SN - 0075-4102
VL - 2002
SP - 33
EP - 39
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 551
ER -