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- Johannes Sprang
- 2018

In this small note, we provide an elementary proof of the fact that infinitely many odd zeta values are irrational. For the first time, this celebrated theorem been proven by Rivoal and Ball--Rivoal.… (More)

Abstract In this note, we announce the following result: at least 2 ( 1 − e ) log s log log s values of the Riemann zeta function at odd integers between 3 and s are irrational, where e is any… (More)

Building upon ideas of the second and third authors, we prove that at least $2^{(1-\varepsilon)\frac{\log s}{\log \log s}}$ values of the Riemann zeta function at odd integers between 3 and $s$ are… (More)

- Johannes Sprang
- 2012

In this note we provide a counterexample to a conjecture due to F. Gouv\^ea, which says that the Krull dimension of the universal deformation ring - as defined by B. Mazur - associated to an… (More)

- Johannes Sprang
- 2013

A well known result of Mazur gives a lower bound for the Krull dimension of the universal deformation ring associated to an absolutely irreducible residual representation in terms of the group… (More)

- Johannes Sprang
- 2018

The celebrated theorem of Ball--Rivoal gives a lower bound for the dimension of the $\mathbb{Q}$-vector space $\mathbb{Q}+\mathbb{Q}\zeta(3)+...+\mathbb{Q}\zeta(s)$ spanned by the odd positive zeta… (More)

- Johannes Sprang
- 2018

A classical construction of Katz gives a purely algebraic construction of real-analytic Eisenstein series using the Gau\ss--Manin connection on the universal elliptic curve. This approach gives a… (More)

The goal of this small note is to extend a result by Christopher Davis and David Zureick-Brown on the comparison between integral Monsky-Washnitzer cohomology and overconvergent de~Rham-Witt… (More)

Building on results of M. Ando, M.J. Hopkins and C. Rezk we show the existence of uncountably many E_\infty-string orientations of KO and tmf. The same holds for E_\infty-spin orientations of KO.… (More)

Building on results of Ando, Hopkins and Rezk, we show the existence of uncountably many $${\mathbb {E}}_\infty $$E∞-String orientations of real K-theory KO and of topological modular forms tmf,… (More)