On Eisenstein series with characters and the values of Dirichlet L-functions
Corrigendum to the paper "Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory"
Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory
Chapter 15 of Ramanujan's Second Notebook: Part 2, Modular forms
A new proof of the reciprocity theorem for Dedekind sums.
Generalized Eisenstein series and modified Dedekind sums.
Chapter 8 of Ramanujan's second notebook.
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Hans Rademacher (1892-1969)
Half Gauss Sums.
Dedekind Sums and Class Numbers.
Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook.
A new class of Bessel function integrals.
Sums involving the greatest integer function and Riemann-Stieltjes integration.
New identities for the Rogers-Ramanujan functions
Congruences for the coefficients of quotients of Eisenstein series
Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary.
Ramanujan's class invariants and cubic continued fraction
Radicals and units in Ramanujan's work
Diophantine approximation with partial sums of power series
We study the question: How often do partial sums of power series of functions coalesce with convergents of the (simple) continued fractions of the functions? Our theorems quantitatively demonstrate that the answer is: not very often. We conjecture that in most cases there are only a finite number of partial sums coinciding with convergents. In many of these cases, we offer exact numbers in our conjectures.
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