The Ramanujan Journal
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The weak Gram law for Hecke $$ L $$ -functions
The Ramanujan Journal - Tập 60 - Trang 981-997 - 2022
We generalize a theorem by Titchmarsh about the mean value of Hardy’s $$Z$$
-function at the Gram points to the Hecke $$L$$ -functions, which in turn
implies the weak Gram law for them. Instead of proceeding analogously to
Titchmarsh with an approximate functional equation we employ a different method
using contour integration....
On index divisors and monogenity of certain number fields defined by $$x^{12}+ax^m+b$$
The Ramanujan Journal - - 2024
On an extension of a van Hamme supercongruence
The Ramanujan Journal - Tập 42 - Trang 713-723 - 2016
We prove a conjectural extension of a van Hamme supercongruence due to Sun. The
proof is inspired by recent techniques due to Osburn and Zudilin, in particular
the use of a certain WZ pair and congruences for quotients of Pochhammer
symbols.
On modular equations of degree 25
The Ramanujan Journal - Tập 56 - Trang 743-752 - 2020
On page 237–238 of his second notebook, Ramanujan recorded five modular
equations of composite degree 25. Berndt proved all these using the method of
parametrization. He also expressed that his proofs undoubtedly often stray from
the path followed by Ramanujan. The purpose of this paper is to give direct
proofs to four of the five modular equations using the identities known to
Ramanujan.
Progress on Olga Taussky-Todd’s circulant problem
The Ramanujan Journal - Tập 28 - Trang 45-60 - 2012
Determining the possible values of integer circulant determinants is an open
problem proposed by Taussky-Todd. Recent interest in this question comes from
studying the Lehmer constant of finite cyclic groups. By refining the approach
by Laquer and Newman we contribute to the circulant determinant problem in the
case that the order is a power of two.
Overpartitions and ternary quadratic forms
The Ramanujan Journal - Tập 42 Số 2 - Trang 429-442 - 2017
Dynamics of a Ramanujan-type continued fraction with cyclic coefficients
The Ramanujan Journal - Tập 16 - Trang 285-304 - 2008
We study several generalizations of the AGM continued fraction of Ramanujan
inspired by a series of recent articles in which the validity of the AGM
relation and the domain of convergence of the continued fraction were determined
for certain complex parameters (Borwein et al., Exp. Math. 13, 275–286, 2004,
Ramanujan J., in press, 2004; Borwein and Crandall, Exp. Math. 12, 287–296,
2004). A study o...
A new proof of the Ramanujan congruences for the partition function
The Ramanujan Journal - Tập 15 Số 2 - Trang 197-204 - 2008
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