TY - JOUR
T1 - Pointwise and correlation bounds on Dedekind sums over small subgroups
AU - Borda, Bence
AU - Munsch, Marc
AU - Shparlinski, Igor E.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
PY - 2024/6
Y1 - 2024/6
N2 - We obtain new bounds, pointwise and on average, for Dedekind sums s(λ,p) modulo a prime p with λ of small multiplicative order d modulo p. Assuming the infinitude of Mersenne primes, the range of our results is optimal. Moreover, we relate high moments of L(1,χ) over subgroups of characters to some correlations of Dedekind sums, and use recent results of the second and third author to study these correlations.
AB - We obtain new bounds, pointwise and on average, for Dedekind sums s(λ,p) modulo a prime p with λ of small multiplicative order d modulo p. Assuming the infinitude of Mersenne primes, the range of our results is optimal. Moreover, we relate high moments of L(1,χ) over subgroups of characters to some correlations of Dedekind sums, and use recent results of the second and third author to study these correlations.
KW - 11F20
KW - 11J71
KW - 11K38
KW - 11M20
KW - Continued fractions
KW - Dedekind sum
KW - L-function
KW - Multiplicative subgroup
UR - http://www.scopus.com/inward/record.url?scp=85187934301&partnerID=8YFLogxK
U2 - 10.1007/s40993-024-00514-9
DO - 10.1007/s40993-024-00514-9
M3 - Article
AN - SCOPUS:85187934301
SN - 2363-9555
VL - 10
JO - Research in Number Theory
JF - Research in Number Theory
IS - 2
M1 - 28
ER -