Fermat's Last Theorem for regular primes

Autor: Best, Alex J., Birkbeck, Christopher, Brasca, Riccardo, Boidi, Eric Rodriguez

We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}. This is an important 19th century result that motivated the development of modern a

Externí odkaz: http://arxiv.org/abs/2305.08955

From Data to Software to Science with the Rubin Observatory LSST

Autor: Breivik, Katelyn, Connolly, Andrew J., Ford, K. E. Saavik, Jurić, Mario, Mandelbaum, Rachel, Miller, Adam A., Norman, Dara, Olsen, Knut, O'Mullane, William, Price-Whelan, Adrian, Sacco, Timothy, Sokoloski, J. L., Villar, Ashley, Acquaviva, Viviana, Ahumada, Tomas, AlSayyad, Yusra, Alves, Catarina S., Andreoni, Igor, Anguita, Timo, Best, Henry J., Bianco, Federica B., Bonito, Rosaria, Bradshaw, Andrew, Burke, Colin J., de Campos, Andresa Rodrigues, Cantiello, Matteo, Caplar, Neven, Chandler, Colin Orion, Chan, James, da Costa, Luiz Nicolaci, Danieli, Shany, Davenport, James R. A., Fabbian, Giulio, Fagin, Joshua, Gagliano, Alexander, Gall, Christa, Camargo, Nicolás Garavito, Gawiser, Eric, Gezari, Suvi, Gomboc, Andreja, Gonzalez-Morales, Alma X., Graham, Matthew J., Gschwend, Julia, Guy, Leanne P., Holman, Matthew J., Hsieh, Henry H., Hundertmark, Markus, Ilić, Dragana, Ishida, Emille E. O., Jurkić, Tomislav, Kannawadi, Arun, Kosakowski, Alekzander, Kovačević, Andjelka B., Kubica, Jeremy, Lanusse, François, Lazar, Ilin, Levine, W. Garrett, Li, Xiaolong, Lu, Jing, Luna, Gerardo Juan Manuel, Mahabal, Ashish A., Malz, Alex I., Mao, Yao-Yuan, Medan, Ilija, Moeyens, Joachim, Nikolić, Mladen, Nikutta, Robert, O'Dowd, Matt, Olsen, Charlotte, Pearson, Sarah, Pedraza, Ilhuiyolitzin Villicana, Popinchalk, Mark, Popović, Luka C., Pritchard, Tyler A., Quint, Bruno C., Radović, Viktor, Ragosta, Fabio, Riccio, Gabriele, Riley, Alexander H., Rożek, Agata, Sánchez-Sáez, Paula, Sarro, Luis M., Saunders, Clare, Savić, Đorđe V., Schmidt, Samuel, Scott, Adam, Shirley, Raphael, Smotherman, Hayden R., Stetzler, Steven, Storey-Fisher, Kate, Street, Rachel A., Trilling, David E., Tsapras, Yiannis, Ustamujic, Sabina, van Velzen, Sjoert, Vázquez-Mata, José Antonio, Venuti, Laura, Wyatt, Samuel, Yu, Weixiang, Zabludoff, Ann

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) dataset will dramatically alter our understanding of the Universe, from the origins of the Solar System to the nature of dark matter and dark energy. Much of this research will depe

Externí odkaz: http://arxiv.org/abs/2208.02781

Elliptic curves with good reduction outside of the first six primes

Autor: Best, Alex J., Matschke, Benjamin

We present a database of rational elliptic curves, up to Q-isomorphism, with good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the abc and BSD conjectures that the database is likely to be the complete set of such curves. Moreo

Externí odkaz: http://arxiv.org/abs/2007.10535

Computing classical modular forms

Autor: Best, Alex J., Bober, Jonathan, Booker, Andrew R., Costa, Edgar, Cremona, John, Derickx, Maarten, Lee, Min, Lowry-Duda, David, Roe, David, Sutherland, Andrew V., Voight, John

Publikováno v: Arithmetic Geometry, Number Theory, and Computation, Simons Symp. (2021), 131-213

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
Comment: 63 pages; minor edits, including a correction to Conjecture 8.5.1

Externí odkaz: http://arxiv.org/abs/2002.04717

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