Results 11 to 20 of about 432 (61)
A computational study of the asymptotic behaviour of coefficient fields of modular forms [PDF]
, 2009 The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fiel ds of modular forms. The observations suggest certain patterns, which deserve further study.
Marcel Mohyla, G. Wiese
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Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
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Vanishing theorems for the mod p cohomology of some simple Shimura varieties
Forum of Mathematics, Sigma, 2020 We show that the mod p cohomology of a simple Shimura variety treated in Harris-Taylor’s book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing
Teruhisa Koshikawa
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EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE
Forum of Mathematics, Sigma, 2019 A classical construction of Katz gives a purely algebraic construction of Eisenstein–Kronecker series using the Gauß–Manin connection on the universal elliptic curve. This approach gives a systematic way to study algebraic and $p$-adic properties of real-
JOHANNES SPRANG
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THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$
Forum of Mathematics, Pi, 2015 Let $p>2$ be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate representations, over arbitrary finite extensions of $\mathbb{Q}_{p}$.
TOBY GEE, TONG LIU, DAVID SAVITT
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On cubic multisections of Eisenstein series [PDF]
, 2013 A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three.
Alaniz, Andrew, Huber, Tim
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On Artin representations and nearly ordinary Hecke algebras over totally real fields
Documenta Mathematica, 2013 We prove many new cases of the strong Artin conjecture for two-dimensional, totally odd, insoluble (icosahedral) representations Gal(F/F ) → GL2(C) of the absolute Galois group of a totally real field F .
Shu Sasaki
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PARALLEL WEIGHT 2 POINTS ON HILBERT MODULAR EIGENVARIETIES AND THE PARITY CONJECTURE
Forum of Mathematics, Sigma, 2019 Let $F$ be a totally real field and let $p$ be an odd prime which is totally split in $F$. We define and study one-dimensional ‘partial’ eigenvarieties interpolating Hilbert modular forms over $F$ with weight varying only at a single place $v$ above $p$.
CHRISTIAN JOHANSSON, JAMES NEWTON
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THE BERNSTEIN CENTER OF THE CATEGORY OF SMOOTH $W(k)[\text{GL}_{n}(F)]$ -MODULES
Forum of Mathematics, Sigma, 2016 We consider the category of smooth $W(k)[\text{GL}_{n}(F)]$ -modules, where $F$
DAVID HELM
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On the freeness of anticyclotomic selmer groups of modular forms [PDF]
, 2016 We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced by Bertolini and Darmon in their work on the anticyclotomic main conjecture ...
Kim, C., Pollack, R., Weston, T.
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