48 citations · 148 across the 10 of their papers we have counts for
13 papers
Computing classical modular forms
Alex J. Best, Jonathan Bober, Andrew R. Booker +8
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
Smooth values of polynomials
Jonathan Bober, Dan Fretwell, Greg Martin +1
Given of positive degree, we investigate the existence of auxiliary polynomials for which factors as a product of polynomials of…
A conjectural extension of Hecke's converse theorem
Sandro Bettin, Jonathan W. Bober, Andrew R. Booker +6
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main…
New computations of the Riemann zeta function on the critical line
Jonathan W. Bober, Ghaith A. Hiary
We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the sec…
The frequency and the structure of large character sums
Jonathan Bober, Leo Goldmakher, Andrew Granville +1
Let denote the maximum of for a given non-principal Dirichlet character , and let denote a point at which the maximum is attained. In t…
Averages of character sums
Jonathan Bober
We show that a short truncation of the Fourier expansion for a character sum gives a good approximation for the average value of that character sum over an interval. We give a few…
Pólya-Vinogradov and the least quadratic nonresidue
Jonathan Bober, Leo Goldmakher
It is well-known that cancellation in short character sums (e.g. Burgess' estimates) yields bounds on the least quadratic nonresidue. Scant progress has been made on short characte…
The highest lowest zero of general L-functions
Jonathan Bober, J. Brian Conrey, David W. Farmer +5
Stephen D. Miller showed that, assuming the generalized Riemann Hypothesis, every entire -function of real archimedian type has a zero in the interval with $-t_0 <…
Conditionally bounding analytic ranks of elliptic curves
Jonathan W. Bober
We describe a method for bounding the rank of an elliptic curve under the assumptions of the Birch and Swinnerton-Dyer conjecture and the generalized Riemann hypothesis. As an exam…
The distribution of the maximum of character sums
Jonathan Bober, Leo Goldmakher
We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal mag…
On a discrete version of Tanaka's theorem for maximal functions
Jonathan Bober, Emanuel Carneiro, Kevin Hughes +1
In this paper we prove a discrete version of Tanaka's Theorem \cite{Ta} for the Hardy-Littlewood maximal operator in dimension , both in the non-centered and centered cases. F…
Bounded step functions and factorial ratio sequences
Jason Bell, Jonathan Bober
We study certain step functions whose nonnegativity is related to the integrality of sequences of ratios of factorial products. In particular, we obtain a lower bound for the mean…
Factorial ratios, hypergeometric series, and a family of step functions
Jonathan Bober
We give a complete classification of a certain family of step functions related to the Nyman--Beurling approach to the Riemann hypothesis and previously studied by V. I. Vasyunin.…