385 citations
- Newcastle UniversityGB60 papers
- Australian National UniversityAU25 papers
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- UNSW SydneyAU21 papers
- Commonwealth Scientific and Industrial Research OrganisationAU19 papers
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- Center for Astrophysics Harvard & SmithsonianUS16 papers
- The University of QueenslandAU16 papers
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- National Astronomical Observatory of JapanJP15 papers
- Centre National de la Recherche ScientifiqueFR14 papers
- Max Planck Institute for AstronomyDE13 papers
48 papers · 1 filter
On some results of Agelas concerning the GRH and of Vassilev-Missana concerning the prime zeta function
Richard P. Brent
A recent paper by Agélas [Generalized Riemann Hypothesis, 2019, hal-00747680v3] claims to prove the Generalized Riemann Hypothesis (GRH) and, as a special case, the Riemann Hypothe…
Lower bounds for periods of Ducci sequences
Florian Breuer, Igor E. Shparlinski
A Ducci sequence is a sequence of integer -tuples obtained by iterating the map \[ D : (a_1, a_2, \ldots, a_n) \mapsto \big(|a_1-a_2|,|a_2-a_3|,\ldots,|a_n-a_1|\big). \] Such a…
Extending the PSLQ Algorithm to Algebraic Integer Relations
Matthew P. Skerritt, Paul Vrbik
The PSLQ algorithm computes integer relations for real numbers and Gaussian integer relations for complex numbers. We endeavour to extend PSLQ to find integer relations consisting…
Drinfeld modular forms of arbitrary rank, Part II: Comparison with Algebraic Theory
Dirk Basson, Florian Breuer, Richard Pink
This is the second of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank. In the present part, we compare the analytic theory wi…
A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
Wadim Zudilin
We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The -th coefficients of the correspon…
A -microscope for supercongruences
Victor J. W. Guo, Wadim Zudilin
By examining asymptotic behavior of certain infinite basic (-) hypergeometric sums at roots of unity (that is, at a "-microscopic" level) we prove polynomial congruences for…