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

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

VL - 2002

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 -