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math.NT2013
Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
Atul Dixit, Victor H. Moll
The classical transformation of Jacobi's theta function admits a simple proof by producing an integral representation that yields this invariance apparent. This idea seems to have…
math.NT2013
Monotonicity Results for Dirichlet L-functions
Atul Dixit, Arindam Roy, Alexandru Zaharescu
We present some monotonicity results for Dirichlet -functions associated to real primitive characters. We show in particular that these Dirichlet -functions are far from bein…
math.NT2013
The Zagier polynomials. Part II: Arithmetic properties of coefficients
Mark W. Coffey, Valerio De Angelis, Atul Dixit +3
The modified Bernoulli numbers \begin{equation*} B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 \end{equation*} introduced by D. Zagier in 1998 were rece…