1 citations · 1 across the 1 of their papers we have counts for
9 papers
Prime geodesics and averages of the Zagier -series
Olga Balkanova, Dmitry Frolenkov, Morten S. Risager
The Zagier -series encode data of real quadratic fields. We study the average size of these -series, and prove asymptotic expansions and omega results for the expansion. We t…
Mixed moment of and -functions
Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov +1
Let run over the space of primitive cusp forms of level one and weight , . We prove an explicit formula for the mixed moment of the Hec…
Prime geodesic theorem for the Picard manifold
Olga Balkanova, Dmitry Frolenkov
Let be the Picard group and be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient , called the Picar…
Sums of Kloosterman sums in the prime geodesic theorem
Olga Balkanova, Dmitry Frolenkov
We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Yo…
Bounds for a spectral exponential sum
Olga Balkanova, Dmitry Frolenkov
We prove new upper bounds for a spectral exponential sum by refining the process by which one evaluates mean values of -functions multiplied by an oscillating function. In parti…
The first moment of cusp form L-functions in weight aspect on average
Olga Balkanova, Dmitry Frolenkov
We study the asymptotic behaviour of the twisted first moment of central -values associated to cusp forms in weight aspect on average. Our estimate of the error term allows exte…