Results 21 to 30 of about 290 (54)

Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

Special Matrices, 2015
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
doaj   +1 more source

Commentary on “Arithmetic on curves” by Barry Mazur

, 2018
Immediately following the commentary below, this previously published article is reprinted in its entirety: B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 207–259.
B. Totaro
semanticscholar   +1 more source

A note on the Mumford-Tate Conjecture for CM abelian varieties

, 2014
The Mumford-Tate conjecture is first proved for CM abelian varieties by H. Pohlmann [Ann. Math., 1968]. In this note we give another proof of this result and extend it to CM motives.Comment: 10 pages, to appear in Taiwanese J ...
Yu, Chia-Fu
core   +1 more source

Supercongruences and Complex Multiplication [PDF]

, 2012
We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime and m, s, r are positive integers.
Kibelbek, Jonas, Long, Ling, Moss, Kevin, Sheller, Benjamin, Yuan, Hao   +4 more
core   +1 more source

On a problem of Hasse and Ramachandra

Open Mathematics, 2019
Let K be an imaginary quadratic field, and let 𝔣 be a nontrivial integral ideal of K. Hasse and Ramachandra asked whether the ray class field of K modulo 𝔣 can be generated by a single value of the Weber function. We completely resolve this question when
Koo Ja Kyung, Shin Dong Hwa, Yoon Dong Sung   +2 more
doaj   +1 more source

Ray class invariants over imaginary quadratic fields

, 2011
Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1.
Jung, Ho Yun, Koo, Ja Kyung, Shin, Dong Hwa   +2 more
core   +1 more source

Large Cyclic Subgroups of Jacobians of Hyperelliptic Curves [PDF]

, 2007
In this paper we obtain conditions on the divisors of the group order of the Jacobian of a hyperelliptic genus 2 curve, generated by the complex multiplication method described by Weng (2003) and Gaudry (2005). Examples, where these conditions imply that
Ravnshoj, Christian Robenhagen
core   +3 more sources

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
doaj   +1 more source

Varieties of sums of powers and moduli spaces of (1,7)-polarized abelian surfaces

, 2017
We study the geometry of some varieties of sums of powers related to the Klein quartic. This allows us to describe the birational geometry of certain moduli spaces of abelian surfaces.
Bolognesi, Michele, Massarenti, Alex
core   +2 more sources

Rigid meromorphic cocycles for orthogonal groups

Forum of Mathematics, Sigma
Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a p-adic analogue of Borcherds’ singular theta lift.
Lennart Gehrmann, Henri Darmon, Michael Lipnowski   +2 more
doaj   +1 more source