The overpartition function modulo 128.
The -adic gamma function and the congruences of Atkin and Swinnerton-Dyer
The -adic measure on the orbit of an element of
The -adic valuations of sequences counting alternating sign matrices.
The -adic -transform
The -part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large
In this paper we show that for every prime the dimension of the -torsion in the Tate-Shafarevich group of can be arbitrarily large, where is an elliptic curve defined over a number field , with bounded by a constant depending only on . From this we deduce that the dimension of the -torsion in the Tate-Shafarevich group of can be arbitrarily large, where is an abelian variety, with bounded by a constant depending only on .
The -rank stratification of Artin-Schreier curves
We study a moduli space for Artin-Schreier curves of genus over an algebraically closed field of characteristic . We study the stratification of by -rank into strata of Artin-Schreier curves of genus with -rank exactly . We enumerate the irreducible components of and find their dimensions. As an application, when , we prove that every irreducible component of the moduli space of hyperelliptic -curves with genus and -rank has dimension . We also determine all pairs for...
The √p Riemann surface
The p-adic differential equation y' = wy in the closed unit disk.
The p-adic L-functions attached to Rankin convolutions of modular forms.
The p-adic valuation of k-central binomial coefficients
The pair correlation of zeros of Dirichlet L-functions and primes in arithmetic progressions.
The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders
Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.
The Pell Sequence of Order K, Multinomial Coefficients, and Probability
The period function of the nonholomorphic Eisenstein series for .
The period lengths of inversive congruential recursions
The period-index problem in WC-groups IV: a local transition theorem
Let be a complete discretely valued field with perfect residue field . Assuming upper bounds on the relation between period and index for WC-groups over , we deduce corresponding upper bounds on the relation between period and index for WC-groups over . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and...
The periods of abelian varieties with complex multiplication and the spectral values of certain zeta functions
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best previously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying our permutation group method to the diophantine study of double integrals of rational functions related to the dilogarithm.
The Perron-Frobenius operator on BV. I.