LEADER 04291nam 22006015 450 001 9910552723303321 005 20251113200114.0 010 $a3-030-80914-5 024 7 $a10.1007/978-3-030-80914-0 035 $a(MiAaPQ)EBC6926794 035 $a(Au-PeEL)EBL6926794 035 $a(CKB)21403469400041 035 $a(PPN)261521527 035 $a(OCoLC)1309053065 035 $a(DE-He213)978-3-030-80914-0 035 $a(EXLCZ)9921403469400041 100 $a20220315d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aArithmetic Geometry, Number Theory, and Computation /$fedited by Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, John Voight 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (587 pages) 225 1 $aSimons Symposia,$x2365-9572 311 08$aPrint version: Balakrishnan, Jennifer S. Arithmetic Geometry, Number Theory, and Computation Cham : Springer International Publishing AG,c2022 9783030809133 320 $aIncludes bibliographical references. 327 $aA robust implementation for solving the S-unit equation and several application (C. Rasmussen) -- Computing classical modular forms for arbitrary congruence subgroups (E. Assaf) -- Square root time Coleman integration on superelliptic curves (A. Best) -- Computing classical modular forms ( A. Sutherland) -- Elliptic curves with good reduction outside of the first six primes (B. Matschke) -- Efficient computation of BSD invariants in genus 2 (R. van Bommel) -- Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (E. Costa) -- Zen and the art of database maintenance (D. Roe) -- Effective obstructions to lifting Tate classes from positive characteristic (E. Costa) -- Conjecture: 100% of elliptic surfaces over Q have rank zero (A. Cowan) -- On rational Bianchi newforms and abelian surfaces with quaternionic multiplication (J. Voight) -- A database of Hilbert modular forms (J. Voight) -- Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB (D. Roe) -- Computing rational points on genus 3 hyperelliptic curves (S. Hashimoto) -- Curves with sharp Chabauty-Coleman bound (S. Gajovi?) -- Chabauty-Coleman computations on rank 1 Picard curves (S. Hashimoto) -- Linear dependence among Hecke eigenvalues (D. Kim) -- Congruent number triangles with the same hypotenuse (D. Lowry-Duda) -- Visualizing modular forms (D. Lowry-Duda) -- A Prym variety with everywhere good reduction over Q(? 61) ( J. Voight) -- The S-integral points on the projective line minus three points via étale covers and Skolem's method (B. Poonen). 330 $aThis volume contains articles related to the work of the Simons Collaboration ?Arithmetic Geometry, Number Theory, and Computation.? The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include ? algebraic varieties over finite fields ? the Chabauty-Coleman method ? modular forms ? rational points on curves of small genus ? S-unit equations and integral points. 410 0$aSimons Symposia,$x2365-9572 606 $aGeometry, Algebraic 606 $aNumber theory 606 $aComputer science 606 $aAlgebraic Geometry 606 $aNumber Theory 606 $aTheory of Computation 615 0$aGeometry, Algebraic. 615 0$aNumber theory. 615 0$aComputer science. 615 14$aAlgebraic Geometry. 615 24$aNumber Theory. 615 24$aTheory of Computation. 676 $a516.35 702 $aBalakrishnan$b Jennifer S 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910552723303321 996 $aArithmetic geometry, number theory, and computation$92960398 997 $aUNINA