Results 11 to 20 of about 284 (57)

Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms

Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 33-48, December 2020., 2020
Abstract We define twisted Eisenstein series Es±(h,k;τ) for s∈C, and show how their associated period functions, initially defined on the upper half complex plane H, have analytic continuation to all of C′:=C∖R⩽0. We also use this result, as well as properties of various zeta functions, to show that certain cotangent‐zeta sums behave like quantum ...
Amanda Folsom
wiley   +1 more source

On class groups of random number fields

Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 927-953, October 2020., 2020
Abstract The main aim of this paper is to disprove the Cohen–Lenstra–Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics.
Alex Bartel, Hendrik W. Lenstra Jr.
wiley   +1 more source

The p-torsion of curves with large p-rank [PDF]

, 2008
Consider the locus of smooth curves of genus g and p-rank f defined over an algebraically closed field k of characteristic p. It is an open problem to classify which group schemes occur as the p-torsion of the Jacobians of these curves for f < g-1.
Pries, Rachel
core   +4 more sources

Groups of generalized G‐type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q

Transactions of the London Mathematical Society, Volume 6, Issue 1, Page 22-52, December 2019., 2019
Abstract Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when changing base to the compositum of all number fields with Galois group G.
Harris B. Daniels, Maarten Derickx, Jeffrey Hatley   +2 more
wiley   +1 more source

Definite orders with locally free cancellation

Transactions of the London Mathematical Society, Volume 6, Issue 1, Page 53-86, December 2019., 2019
Abstract We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.
Daniel Smertnig, John Voight
wiley   +1 more source

Krein-space operators determined by free product algebras induced by primes and graphs

Special Matrices, 2017
In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
doaj   +1 more source

Degeneration of Hodge structures over Picard modular surfaces [PDF]

, 2017
We study variations of Hodge structures over a Picard modular surface, and compute the weights and types of their degenerations through the cusps of the Baily-Borel compactification.
Ancona, Giuseppe
core   +1 more source

COMPACTIFICATIONS OF PEL-TYPE SHIMURA VARIETIES IN RAMIFIED CHARACTERISTICS

Forum of Mathematics, Sigma, 2016
We show that, by taking normalizations over certain auxiliary good reduction integral models, one obtains integral models of toroidal and minimal compactifications of PEL-type Shimura varieties which enjoy many features of the good reduction theory ...
KAI-WEN LAN
doaj   +1 more source

On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

Open Mathematics, 2019
After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
doaj   +1 more source

COMPACTIFICATIONS OF SUBSCHEMES OF INTEGRAL MODELS OF SHIMURA VARIETIES

Forum of Mathematics, Sigma, 2018
We study several kinds of subschemes of mixed characteristic models of Shimura varieties which admit good (partial) toroidal and minimal compactifications, with familiar boundary stratifications and formal local structures, as if they were Shimura ...
KAI-WEN LAN, BENOÎT STROH
doaj   +1 more source