TY - JOUR

T1 - On the vanishing of some mock theta functions at odd roots of unity

AU - El Bachraoui, Mohamed

N1 - Funding Information:
The author is grateful for the referee for valuable comments and suggestions which improved the quality and the presentation of the paper. The final draft of this work has been completed in the summer of 2021 while visiting my birthplace Nador. I thank Novo Class Café in Nador and its staff for the great environment, the high speed internet, and the top quality coffee.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2021/9

Y1 - 2021/9

N2 - We consider the problem of whether or not certain mock theta functions vanish at the roots of unity with an odd order. We prove for any such function f(q) that there exists a constant C> 0 such that for any odd integer n> C the function f(q) does not vanish at the primitive n-th roots of unity. This leads us to conjecture that f(q) does not vanish at the primitive n-th roots of unity for any odd positive integer n.

AB - We consider the problem of whether or not certain mock theta functions vanish at the roots of unity with an odd order. We prove for any such function f(q) that there exists a constant C> 0 such that for any odd integer n> C the function f(q) does not vanish at the primitive n-th roots of unity. This leads us to conjecture that f(q) does not vanish at the primitive n-th roots of unity for any odd positive integer n.

KW - Mock theta functions

KW - Q-series

KW - Vanishing sums of roots of unity

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U2 - 10.1007/s40993-021-00279-5

DO - 10.1007/s40993-021-00279-5

M3 - Article

AN - SCOPUS:85111510533

VL - 7

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 3

M1 - 50

ER -