Article
Mathematics
Maximilian Schmidt
Summary: The understanding of Seshadri constants on abelian surfaces is limited to cases with Picard number one and principally polarized abelian surfaces with real multiplication. Partial results exist for products of elliptic curves. This paper presents a method to compute the Seshadri constant of any nef line bundle on any abelian surface over the complex numbers, utilizing an effective algorithm based on the Neron-Severi group. The access to Seshadri curves allows for the plotting of Seshadri functions, revealing their varying complexity even in the case of Picard number two.
ADVANCES IN MATHEMATICS
(2023)
Article
Multidisciplinary Sciences
Qinghua Guo, Tianshu Jiang, Ruo-Yang Zhang, Lei Zhang, Zhao-Qing Zhang, Biao Yang, Shuang Zhang, C. T. Chan
Summary: Experimental observation of non-Abelian topological charges and edge states in a PT-symmetric transmission line network, along with the discovery of a non-Abelian quotient relation for the bulk-edge correspondence. This new topological property opens up possibilities for intriguing observable phenomena in the field of material science.
Article
Mathematics, Applied
Wolfgang Ebeling, Sabir M. Gusein-Zade
Summary: This article studies the Berglund-Hubsch-Henningson-Takahashi duality of Landau-Ginzburg orbifolds with a symmetry group generated by diagonal symmetries and permutations of variables. The orbifold Euler characteristics, orbifold monodromy zeta functions, and orbifold E-functions of such dual pairs are examined. The conjecture is made that mirror symmetry exists between these invariants at every level, with level being defined as the conjugacy class of a permutation. Partial results for each of these invariants are provided to support this conjecture.
JOURNAL OF GEOMETRY AND PHYSICS
(2022)
Article
Mathematics
Dhairya Shah, Manoj Sahni, Ritu Sahni, Ernesto Leon-Castro, Maricruz Olazabal-Lugo
Summary: In this second part of a series of papers, we extend the theorems discussed in the first part to infinite series. We then use these theorems to derive new results involving different mathematical functions. We also investigate the behavior of these newly developed functions and provide examples showcasing the broad scope and potential of the theorems in creating a new field under the realm of number theory and analysis.
Article
Mathematics, Applied
Vishal Arul, Jeremy Booher, Steven R. Groen, Everett W. Howe, Wanlin Li, Vlad Matei, Rachel Pries, Caleb Springer
Summary: We study the characteristics of curves over finite fields and their covering curves through their zeta functions. We investigate the phenomenon of the number of doubly isogenous curves exceeding naïve heuristics predictions, and provide an explanation for this in the case of genus 2 curves with automorphism groups containing the dihedral group of order eight.
MATHEMATICS OF COMPUTATION
(2023)
Article
Mathematics
Laurent Buse, Alexandru Dimca, Hal Schenck, Gabriel Sticlaru
Summary: We study the regularity of the Milnor algebra M(f) when the reduced hypersurface V(f) has a positive dimensional singular locus. In certain situations, we prove that the regularity is bounded by (d-2)(n+1), while in P-n, the regularity of the Milnor algebra can grow quadratically in d.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics
Michael J. Griffin, Ken Ono, Larry Rolen, Jesse Thorner, Zachary Tripp, Ian Wagner
Summary: This paper investigates the influence of the zeros of xi(s) and its derivatives on the hyperbolicity of Jensen polynomials.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics
Everett W. Howe
Summary: The Oesterle bound states that a curve of genus 8 over the finite field F4 can have at most 24 rational points, but this study shows that such a curve can actually have at most 23 rational points, and provides an example of a curve with 22 points.
JOURNAL OF NUMBER THEORY
(2021)
Article
Mathematics
Nianliang Wang, Kalyan Chakraborty, Shigeru Kanemitsu
Summary: Chowla's inverse problem (CP) aims to prove the linear independence of cotangent-like values based on the non-vanishing of L(1,chi) = n-ary sumation n=1 & INFIN;chi(n)n. Moreover, the determinant expressions for the (relative) class number of a cyclotomic field are referred to as Maillet-Demyanenko determinants (MD). Our objective is to develop the theory of discrete Fourier transforms (DFT) with parity and unify Chowla's problem and Maillet-Demyanenko determinants (CPMD) as different appearances of the relative class number using the Dedekind determinant and the base change formula.
Article
Mathematics, Applied
Filipe Fernandes
Summary: This note presents the example with the lowest degree known so far of a non-injective local polynomial diffeomorphism. The construction is based on a celebrated counterexample to the real Jacobian conjecture by S. Pinchuk.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Yanlin Li, Kemal Eren, Kebire Hilal Ayvaci, Soley Ersoy
Summary: This study introduces partner ruled surfaces based on the Flc frame defined on a polynomial curve. The conditions for each couple of partner ruled surfaces to be simultaneously developable and minimal are investigated. Furthermore, the asymptotic, geodesic and curvature lines of the parameter curves of the partner ruled surfaces are simultaneously characterized.
Article
Mathematics
Alexandru Dimca, Giovanna Ilardi, Gabriel Sticlaru
Summary: This paper mainly studies the relationship between the important invariant mdr(f) of a reduced curve C in the complex projective plane and the decomposition of C as well as its singularities. Some geometric criteria are derived to determine whether a line is a jumping line for the rank 2 vector bundle of logarithmic vector fields along C.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics, Applied
Sven Bootsma, Saeed Tafazolian, Jaap Top
Summary: We study a specific type of elliptic surfaces defined by the equation y2 = x3 + f (t)x, over the finite field Fq for a prime power q -3 mod 4. The rank of the group of sections on the elliptic surface over Fq can be determined based on elementary properties of the rational function f(t) if the curve defined by s4 = f(t) is maximal over Fq2. Similar results are shown for elliptic surfaces given by y2 = x3 + g(t) using prime powers q -5 mod 6 and curves s6 = g(t). The existence of maximal curves over Fq2 and various examples are also discussed.
FINITE FIELDS AND THEIR APPLICATIONS
(2023)
Article
Mathematics
Robert Reynolds, Allan Stauffer
Summary: This paper utilizes a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. It provides formulae for various classes of infinite sums of the Euler polynomial using the Riemann Zeta function and fundamental mathematical constants, including Catalan's constant. The representation of Catalan's constant suggests the possibility of it being rational.
Article
Mathematics
Aidas Balciunas, Mindaugas Jasas, Renata Macaitiene, Darius Siauciunas
Summary: This paper considers two periodic sequences of complex numbers, a = {a(m)} and b = {b(m)}, where a is multiplicative. The joint approximation of a pair of analytic functions is studied through shifts (zeta(nT)(s + it; a), zeta(nT)(s + it, alpha; b)) of absolutely convergent Dirichlet series zeta(nT)(s; a) and zeta(nT)(s, alpha; b), involving the sequences a and b. It is proved that the set of these shifts in the interval [0, T] has a positive density, which generalizes and extends the Mishou joint universality theorem for the Riemann and Hurwitz zeta-functions.
Article
Mathematics, Applied
Reinier Broeker, Everett W. Howe, Kristin E. Lauter, Peter Stevenhagen
LMS JOURNAL OF COMPUTATION AND MATHEMATICS
(2015)
Article
Mathematics
Everett W. Howe
JOURNAL OF NUMBER THEORY
(2016)
Article
Mathematics, Applied
Everett W. Howe
FINITE FIELDS AND THEIR APPLICATIONS
(2017)
Article
Mathematics
Ken McMurdy, Robert Coleman
ALGEBRA & NUMBER THEORY
(2010)
Article
Mathematics
Everett W. Howe
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2015)
Article
Mathematics, Applied
Vassil S. Dimitrov, Everett W. Howe
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2011)
Article
Mathematics, Applied
Noam D. Elkies, Everett W. Howe, Christophe Ritzenthaler
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2014)
Article
Mathematics
Everett W. Howe
Summary: The Oesterle bound states that a curve of genus 8 over the finite field F4 can have at most 24 rational points, but this study shows that such a curve can actually have at most 23 rational points, and provides an example of a curve with 22 points.
JOURNAL OF NUMBER THEORY
(2021)
Article
Mathematics
Everett W. Howe, Kiran S. Kedlaya
Summary: Through the proof, we show that for every integer m greater than 0, there exists an ordinary abelian variety over F-2 with exactly m rational points.
RESEARCH IN NUMBER THEORY
(2021)
Proceedings Paper
Mathematics
Jeffrey D. Achter, Everett W. Howe
ARITHMETIC GEOMETRY: COMPUTATION AND APPLICATIONS
(2019)
Article
Mathematics
Jeffrey D. Achter, Everett W. Howe
ALGEBRA & NUMBER THEORY
(2017)
Proceedings Paper
Mathematics
Everett W. Howe
FROBENIUS DISTRIBUTIONS: LANG-TROTTER AND SATO-TATE CONJECTURES
(2016)
Proceedings Paper
Mathematics
Everett W. Howe, Kristin E. Lauter
GEOMETRY AND ARITHMETIC
(2012)
Proceedings Paper
Mathematics
Everett W. Howe
ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY
(2012)
