Rank zero quadratic twists of modular elliptic curves
Parity of the partition function in arithmetic progressions.
On the positivity of the number of t-core partitions
A partition of a positive integer n is a nonincreasing sequence of positive integers with sum Here we define a special class of partitions. 1. Let be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3,4,6]. If and , then we define...
Tate-Shafarevich groups of the congruent number elliptic curves
Euler's concordant forms
4-core partitions and class numbers
Identities for traces of singular moduli
Arithmetic of certain hypergeometric modular forms
Divisibility criteria for class numbers of imaginary quadratic fields
On the representation of integers as sums of triangular numbers.
Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve
Distribution of the partition function modulo .
Parity of the partition function.
The arithmetic of the coefficients of half-integral weight Eisenstein series
Probabilities as values of modular forms and continued fractions.
Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary.
A binomial coefficient identity associated to a conjecture of Beukers.
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