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5 papers · 2 filters
Bounding in the critical strip
Emanuel Carneiro, Vorrapan Chandee
Assuming the Riemann Hypothesis, we make use of the recently discovered \cite{CLV} extremal majorants and minorants of prescribed exponential type for the function $\log\left(\tfra…
Rings and ideals parametrized by binary n-ic forms
Melanie Matchett Wood
The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to…
Gauss composition over an arbitrary base
Melanie Matchett Wood
The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given…
Quartic rings associated to binary quartic forms
Melanie Matchett Wood
We give a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring, relating the rings associated to binary quartic forms with Bhargava's cubi…
An asymptotic expansion related to the Dickman function
K. Soundararajan
We prove a conjecture of Broadurst (arXiv:1004.0519v1) on asymptotic expansions of certain polylogarithm type functions related to the Dickman function.