• Vivek V Rane

Articles written in Proceedings – Mathematical Sciences

• A new approximate functional equation for Hurwitz zeta function for rational parameter

For Hurwitz zeta function ζ(s, (a/k)) witha = 1,2,3,…,k, we obtain a new simple approximate functional equation (uniform ink andt) in critical strip. Our method should prove to be an alternative approach to Atkinson’s method in dealing with$$\sum\nolimits_{x(\bmod q)} {\int_0^T {|L(s,x)|^2 } } dt$$, whereL(s, x) is Dirichlet L-series moduloq and s = σ +it.

• Analogues of Euler and Poisson summation formulae

Euler-Maclaurin and Poisson analogues of the summations εa &lt;nb χ(n)f(n), have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence;d(n) is the divisor function andf(x) is a sufficiently smooth function on [a, b]. We also state a generalised Abel’s summation formula, generalised Euler’s summation formula and Euler’s summation formula in several variables.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

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