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Manjul Bhargava

Princeton University0009-0002-5572-5204
math.NTmath.AGmath.RTmath.ACmath.COmath.GRmath.LO

On Valency

published · living versions
W_3dwvdqrp·v1 · currentpublished
Cyclic reductions of elliptic curves at a positive proportion of primes
1 version

Preprints & journals

55 papers in the corpus · 2010–2026
The existence of small defining polynomials for number fields2610.20600v1 · Manjul Bhargava, Sameera Vemulapalli2026 · 0 citationsarXiv
The existence and uniqueness of magic-faced hypercubes, and applications to Khajuraho most-perfect magic squares, cubes, and hypercubes2609.26762v1 · Manjul Bhargava2026 · 0 citationsarXiv
Geometry-of-numbers methods over global fields II: Coregular representations2604.16978v1 · Manjul Bhargava, Arul Shankar, Xiaoheng Wang2026 · 0 citationsarXiv
The existence of infinitely many cubic fields with class group of exact 2-rank 12602.06894v1 · Manjul Bhargava, Arul Shankar, Artane Siad et al.2026 · 0 citationsarXiv
The second moment of the size of the 22-class group of monogenized cubic fields2506.05539v1 · Manjul Bhargava, Arul Shankar, Ashvin Swaminathan2025 · 0 citationsarXiv
Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field2501.18774v1 · Levent Alpoge, Manjul Bhargava, Wei Ho et al.2025 · 4 citationsarXiv
A proof of van der Waerden's Conjecture on random Galois groups of polynomials2410.03792v2 · Manjul Bhargava2024 · 4 citationsarXiv
Integers expressible as the sum of two rational cubes2210.10730v3 · Levent Alpoge, Manjul Bhargava, Ari Shnidman (with an appendix by Ashay Burungale et al.2022 · 3 citationsarXiv
Squarefree values of polynomial discriminants II2207.05592v1 · Manjul Bhargava, Arul Shankar, Xiaoheng Wang2022 · 8 citationsForum of Mathematics, Pi 13 (2025) e17
On average sizes of Selmer groups and ranks in families of elliptic curves having marked points2207.03309v2 · Manjul Bhargava, Wei Ho2022 · 4 citationsarXiv
An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree2204.01331v2 · Manjul Bhargava, Arul Shankar, Xiaoheng Wang2022 · 5 citationsarXiv
Galois groups of random integer polynomials and van der Waerden's Conjecture2111.06507v3 · Manjul Bhargava2021 · 11 citationsarXiv
On the number of monogenizations of a quartic order2111.04215v2 · Manjul Bhargava (with an appendix by Shabnam Akhtari)2021 · 0 citationsarXiv
The second moment of the size of the 22-Selmer group of elliptic curves2110.09063v1 · Manjul Bhargava, Arul Shankar, Ashvin Swaminathan2021 · 2 citationsarXiv
Hermite equivalence of polynomials2109.02932v3 · Manjul Bhargava, Jan-Hendrik Evertse, K'alm'an Gyory et al.2021 · 2 citationsActa Arithmetica, on-line first, 2023
Improved error estimates for the Davenport-Heilbronn theorems2107.12819v2 · Manjul Bhargava, Takashi Taniguchi, Frank Thorne2021 · 8 citationsarXiv
A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so2107.05514v1 · Levent Alpoge, Manjul Bhargava, Ari Shnidman2021 · 6 citationsarXiv
The density of polynomials of degree nn over Zp\mathbb{Z}_p having exactly rr roots in Qp\mathbb{Q}_p2101.09590v4 · Manjul Bhargava, John Cremona, Tom Fisher et al.2021 · 1 citationarXiv
A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so2011.01186v2 · Levent Alpoge, Manjul Bhargava, Ari Shnidman2020 · 3 citationsarXiv
The mean number of 2-torsion elements in the class groups of nn-monogenized cubic fields2010.15744v1 · Manjul Bhargava, Jonathan Hanke, Arul Shankar2020 · 4 citationsarXiv
The local-global principle for integral points on stacky curves2006.00167v1 · Manjul Bhargava, Bjorn Poonen2020 · 5 citationsarXiv
The proportion of genus one curves over Q\mathbb{Q} defined by a binary quartic that everywhere locally have a point2004.12085v3 · Manjul Bhargava, John Cremona, Tom Fisher2020 · 3 citationsarXiv
Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families1904.00116v1 · Manjul Bhargava, Zev Klagsbrun, Robert J. Lemke Oliver et al.2019 · 9 citationsAlg. Number Th. 15 (2021) 627-655
Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves1701.02458v1 · Manjul Bhargava, Arul Shankar, Takashi Taniguchi et al.2017 · 53 citationsarXiv
Squarefree values of polynomial discriminants I1611.09806v3 · Manjul Bhargava, Arul Shankar, Xiaoheng Wang2016 · 69 citationsarXiv
The average size of the 3-isogeny Selmer groups of elliptic curves y2=x3+ky^2 = x^3 + k1610.05759v1 · Manjul Bhargava, Noam Elkies, Ari Shnidman2016 · 23 citationsarXiv
A positive proportion of Thue equations fail the integral Hasse principle1603.08623v3 · Shabnam Akhtari, Manjul Bhargava2016 · 10 citationsarXiv
Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces1512.03035v2 · Manjul Bhargava, Arul Shankar, Xiaoheng Wang2015 · 21 citationsarXiv
What is the probability that a random integral quadratic form in nn variables has an integral zero?1502.05992v1 · M. Bhargava, J. E. Cremona, T. A. Fisher et al.2015 · 7 citationsarXiv
A majority of elliptic curves over Q\mathbb Q satisfy the Birch and Swinnerton-Dyer conjecture1407.1826v2 · Manjul Bhargava, Christopher Skinner, Wei Zhang2014 · 19 citationsarXiv
On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields1402.5738v1 · Manjul Bhargava, Ila Varma2014 · 28 citationsDuke Math. J. 164, no. 10 (2015), 1911-1933
A positive proportion of plane cubics fail the Hasse principle1402.1131v1 · Manjul Bhargava2014 · 27 citationsarXiv
The geometric sieve and the density of squarefree values of invariant polynomials1402.0031v1 · Manjul Bhargava2014 · 44 citationsarXiv
The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders1401.5875v1 · Manjul Bhargava, Ila Varma2014 · 27 citationsarXiv
A positive proportion of elliptic curves over Q\mathbb{Q} have rank one1401.0233v1 · Manjul Bhargava, Christopher Skinner2014 · 4 citationsarXiv
The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 11312.7859v1 · Manjul Bhargava, Arul Shankar2013 · 43 citationsarXiv
The average number of elements in the 4-Selmer groups of elliptic curves is 71312.7333v1 · Manjul Bhargava, Arul Shankar2013 · 26 citationsarXiv
On the number of integral binary nn-ic forms having bounded Julia invariant1312.7339v2 · Manjul Bhargava, Andrew Yang2013 · 4 citationsarXiv
Orbit Parametrizations for K3 Surfaces1312.0898v2 · Manjul Bhargava, Wei Ho, Abhinav Kumar2013 · 11 citationsForum Math. Sigma 4 (2016), e18, 86 pp
What is the probability that a random integral quadratic form in nn variables is isotropic?1311.5543v2 · Manjul Bhargava, John Cremona, Tom Fisher2013 · 2 citationsarXiv
The proportion of plane cubic curves over Q{\mathbb Q} that everywhere locally have a point1311.5578v1 · Manjul Bhargava, John Cremona, Tom Fisher2013 · 2 citationsarXiv
Arithmetic invariant theory II1310.7689v1 · Manjul Bhargava, Benedict H. Gross, Xiaoheng Wang2013 · 0 citationsarXiv
A positive proportion of locally soluble hyperelliptic curves over Q\mathbb Q have no point over any odd degree extension1310.7692v2 · Manjul Bhargava, Benedict H. Gross, Xiaoheng Wang (with an appendix by Tim et al.2013 · 38 citationsarXiv
The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields1309.2025v2 · Manjul Bhargava, Piper Harron2013 · 20 citationsCompositio Math. 152 (2016) 1111-1120
Most hyperelliptic curves over Q have no rational points1308.0395v1 · Manjul Bhargava2013 · 34 citationsarXiv
Coregular spaces and genus one curves1306.4424v1 · Manjul Bhargava, Wei Ho2013 · 45 citationsarXiv
Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves1304.3971v2 · Manjul Bhargava, Daniel M. Kane, Hendrik W. Lenstra jr. et al.2013 · 63 citationsCamb. J. Math. 3 (2015), no. 3, 275-321
The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point1208.1007v2 · Manjul Bhargava, Benedict H. Gross2012 · 60 citationsarXiv
On the number of cubic orders of bounded discriminant having automorphism group C3C_3, and related problems1206.4746v2 · Manjul Bhargava, Ariel Shnidman2012 · 23 citationsAlgebra Number Theory 8 (2014) 53-88
Arithmetic invariant theory1206.4774v2 · Manjul Bhargava, Benedict H. Gross2012 · 46 citationsarXiv
Career total: 100 works. 55 are in this corpus.Showing the 50 most recent.

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