From the 1 of 5 linked papers with an AI index.
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Large sieve inequality for sums of Legendre symbols over short intervals
Marc Munsch, Igor Shparlinski, Yu-Chen Sun +1
The paper establishes a nontrivial upper bound for the second moment of sums of Legendre symbols over short intervals using the Burgess bound and Selberg sieve, showing that for mo…
Small values of signed harmonic sums and logarithmic means of multiplicative functions
Oleksiy Klurman, Marc Munsch, Yu-Chen Sun
We construct sequences with small values of signed harmonic sums \[ \sum_{n\in\mathcal{A}\cap[1,N]}\frac{a_n}{n}, \] for any reas…
Large values of for subgroups of characters
Pranendu Darbar, Bryce Kerr, Marc Munsch +1
We obtain (conditional and unconditional) results on large values of -functions in the critical strip when the character runs through a th…
Bounds for moments of quadratic character sums and theta functions
Marc Munsch, Yuichiro Toma
In this paper, we investigate the size of moments of quadratic character sums averaged over the family of fundamental discriminants. We obtain an asymptotic formula for all integer…
Moments and non-vanishing of -functions over thin subgroups
Marc Munsch, Igor E. Shparlinski
We obtain an asymptotic formula for all moments of Dirichlet -functions modulo when averaged over a subgroup of characters of size with $Ï(d)=o(\lo…
Sign changes of short character sums and real zeros of Fekete polynomials
Oleksiy Klurman, Youness Lamzouri, Marc Munsch
We discuss a general approach producing quantitative bounds on the number of sign changes of the weighted sums where is a fami…