TY - JOUR

T1 - An integral of Dedekind eta-functions in Ramanujan's lost notebook

AU - Berndt, Bruce C.

AU - Zaharescu, Alexandru

PY - 2002/12/1

Y1 - 2002/12/1

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 different 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 different proof of this result which also shows that Ramanujan's questioned formula for C is correct.

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M3 - Article

AN - SCOPUS:0042168812

SP - 33

EP - 39

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 551

ER -