16 citations · 47 across the 41 of their papers we have counts for
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Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Tewodros Amdeberhan, Leonid G. Fel, Ken Ono
Ramanujan derived a sequence of even weight quasimodular forms from derivatives of Jacobi's weight theta function. Using the generating function for this seq…
Semigroup's series for negative degrees of the gaps values in numerical semigroups generated by two integers and identities for the Hurwitz zeta functions
Leonid G. Fel, Takao Komatsu
We derive an explicit expression for an inverse power series over the gaps values of numerical semigroups generated by two integers. It implies a set of new identities for the Hurw…
Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization
Leonid G. Fel
We consider a wide class of summatory functions F{f;N,p^m}=\sum_{k\leq N}f(p^m k), m\in \mathbb Z_+\cup {0}, associated with the multiplicative arithmetic functions f of a scaled v…
On Numerical Experiments with Symmetric Semigroups Generated by Three Elements and Their Generalization
Leonid G. Fel
We give a simple explanation of numerical experiments of V. Arnold with two sequences of symmetric numerical semigroups, S(4,6+4k,87-4k) and S(9,3+9k,85-9k) generated by three elem…
Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
Leonid G. Fel
The symmetric numerical semigroups S(F_a,F_b,F_c) and S(L_k,L_m,L_n) generated by three Fibonacci (F_a,F_b,F_c) and Lucas (L_k,L_m,L_n) numbers are considered. Based on divisibilit…
On Summatory Totient Functions
Leonid G. Fel
The lower and upper bounds are found for the leading term of summatory totient function in various ranges of and .